user135: This answer points out that Karma is not something which is accumulated. 
Hence considering karma as just cause & effect, if I undergo suffering now, like disease, disability, etc, will my future births be better since the cause has yielded a result and that cause is exhausted and will not influence my future births any more. So more suffering I undergo now, more causes I am exhausting ? 

user70: If an individual is suffering because they are overcoming the five hindrances than probably. If a person is suffering because they are indulging in the five hindrances than probably not.
If I eat a big plate of my favorite food every night I will suffer from it because there will be times when I am not eating it, there are times I will feel sick from too much of it and many other ills associated with the indulgence. This suffering (unless it leads to the eventual cessation of desire in regards to this food) will not help my future births.
If I am addicted to eating my favorite food every night and I realize how foolish it is to indulge in it, and I decided to stop, I will suffer during the process of overcoming this attachment. This suffering will help my future births.
In regards to OP's comment: A person who recently got a disease would not have any more inherent suffering in their life than someone who did not have a disease given that they are clear of the hindrances. 
The suffering is compounded when the individual desires feeling good and healthy (sensory desire), or is worried about death or further illness (worry), or is angry that they are sick when someone else they know deserves it more (ill-will), etc, etc.... That type of suffering, the same as in the example regarding food, will not help; overcoming attachments to these hindrances can incur a lot of suffering (I am not my good health, I am not worried about "death", no one deserves anything, etc, etc...; respectively) and that suffering can help future rebirths.

user92: Since there are great answers already, I won't be answering. So consider this not as an answer but as an appendix that might help you discern the details of the answers.

MN 14, The Shorter Discourse on the Mass of Suffering (Cūḷadukkhakkhandha-suttaṃ)
MN 45, The Shorter Discourse on Ways of Undertaking Things (Cūḷadhammasamādāna-suttaṃ) *
MN 46, The Greater Discourse on Ways of Undertaking Things (Mahādhammasamādāna-suttaṃ) *
MN 101, To Devadaha (Devadaha-suttaṃ) 

* These discourses seem to answer the question directly.

user43: Devadaha Sutta (MN 101) linked to by @Yuttadhamo is the right sutra to consider, that fully covers this topic. As you can see in MN 101, the Jains too held position that "burning" past karma through exertion and austerity can lead to liberation.
As he interrogates Jains, Buddha makes following points:

Not all pain comes from causes in the past. Some pain obviously comes from fierce striving, fierce exertion performed in the here-and-now. (As my first teacher used to say, sometimes pain comes from dental crowns and not from karma.)
Unfortunately, we can't really see how much negative karma we have accumulated, and how much karma has been exhausted so far.
If we saw that, then in theory we could talk about removing karma through exertion, similarly to how surgeon removes a poisoned arrow, producing pain short-term, but stopping it long-term.
Unfortunately, that is not possible, because: 

Unfruitted karma that is to fruit in one way, cannot be converted to fruit in another way, through striving & exertion.
Unfruitted karma that is to fruit in the future, cannot be converted to fruit in the present, and vice versa, through striving & exertion.
Unfruitted karma that is to bring result of one size, cannot be converted to bring result of another size, through striving & exertion.


Instead, according to Buddha's teaching in MN 101, liberation from dukkha is achieved by "abandoning of unskillful mental qualities and the attainment of skillful mental qualities in the here-&-now".
Specifically, "skillful mental qualities" refer to 1) "exertion of fabrication against a cause of dukkha" which leads to "dispassion due to the fabrication", and to 2) "looking with equanimity at the cause of dukkha", which leads to "dispassion through the development of equanimity". In other words, cessation of dukkha is attained through 1) deliberate control of one's perspective, and through 2) equanimity that comes from philosophical attitude.
As an example of typical dukkha-pattern, Buddha tells a story of unshared love, with the protagonist suffering from "sorrow, lamentation, pain, distress, & despair" due to being "in love with her, his mind ensnared with fierce desire, fierce passion". The protagonist then wilfully abandons "desire & passion for that woman" (an effort that serves as "exertion of fabrication against a cause of dukkha") and as a result attains dispassion "due to the fabrication".
With all of the above in mind, Buddha still admits to importance of pushing oneself and overcoming one's limits -- to avoid regress due to indulgence -- but only inasmuch as to have "unskillful qualities decline" and "skillful qualities increase":

So he exerts himself with stress & pain, and while he is exerting
  himself with stress & pain, unskillful qualities decline in him, &
  skillful qualities increase. Then at a later time he would no longer
  exert himself with stress & pain. Why is that? Because he has attained
  the goal for which he was exerting himself with stress & pain.

As a result, 

A monk, when not loaded down, does not load himself down with pain,
  nor does he reject pleasure that accords with the Dhamma, although he
  is not fixated on that pleasure.


user18: I never really understood this view, but it seems to have been held by the Niganthas. See MN 101 for a detailed argument against this sort of reasoning (too long to quote here).
Basically, though, it is like saying that if I have taken poison, I should take more poison so I feel the poisoning more quickly and thus somehow work out the result of the original poison quicker. Isn't that a ridiculous idea?
If I have performed karma X in the past that has result A in the future, performing other karmas Y and Z that also have result A doesn't do anything (except perhaps coincidentally - e.g. cutting off my arm means I can't experience pain in my hand) to affect karma X.
Another fallacy here is the idea that experiencing suffering leads to future happiness (in a way that pleasure doesn't). Really, to be objective, your question would have to include pleasure, in which case it would be, "If I undergo pleasure and pain in this life, will my next rebirth be better?" to which the answer is of course no. 
An important concept to always keep in mind, according to the Buddha's teaching, is that pleasure and pain don't lead to pleasure or pain, it is good and evil that lead to pleasure and pain.

135: <p><a href="https://buddhism.stackexchange.com/a/1430/135">This</a> answer points out that Karma is not something which is accumulated. </p>

<p>Hence considering karma as just cause &amp; effect, if I undergo suffering now, like disease, disability, etc, will my future births be better since the cause has yielded a result and that cause is exhausted and will not influence my future births any more. So more suffering I undergo now, more causes I am exhausting ? </p>
 70: <p>If an individual is suffering because they are overcoming the five hindrances than probably. If a person is suffering because they are indulging in the five hindrances than probably not.</p>

<p>If I eat a big plate of my favorite food every night I will suffer from it because there will be times when I am not eating it, there are times I will feel sick from too much of it and many other ills associated with the indulgence. This suffering (unless it leads to the eventual cessation of desire in regards to this food) will not help my future births.</p>

<p>If I am addicted to eating my favorite food every night and I realize how foolish it is to indulge in it, and I decided to stop, I will suffer during the process of overcoming this attachment. This suffering will help my future births.</p>

<p>In regards to OP's comment: A person who recently got a disease would not have any more inherent suffering in their life than someone who did not have a disease given that they are clear of the hindrances. </p>

<p>The suffering is compounded when the individual desires feeling good and healthy (sensory desire), or is worried about death or further illness (worry), or is angry that they are sick when someone else they know deserves it more (ill-will), etc, etc.... That type of suffering, the same as in the example regarding food, will not help; overcoming attachments to these hindrances can incur a lot of suffering (I am not my good health, I am not worried about "death", no one deserves anything, etc, etc...; respectively) and that suffering can help future rebirths.</p>
 92: <p>Since there are great answers already, I won't be answering. So consider this not as an answer but as an appendix that might help you discern the details of the answers.</p>

<ul>
<li><em><a href="http://lirs.ru/lib/sutra/The_Middle_Length_Discourses(Majjhima_Nikaya),Nanamoli,Bodhi,1995.pdf#page=188" rel="nofollow noreferrer">MN 14, The Shorter Discourse on the Mass of Suffering (Cūḷadukkhakkhandha-suttaṃ)</a></em></li>
<li><a href="http://lirs.ru/lib/sutra/The_Middle_Length_Discourses(Majjhima_Nikaya),Nanamoli,Bodhi,1995.pdf#page=407" rel="nofollow noreferrer"><em>MN 45, The Shorter Discourse on Ways of Undertaking Things (Cūḷadhammasamādāna-suttaṃ)</em></a> <sup>*</sup></li>
<li><em><a href="http://lirs.ru/lib/sutra/The_Middle_Length_Discourses(Majjhima_Nikaya),Nanamoli,Bodhi,1995.pdf#page=410" rel="nofollow noreferrer">MN 46, The Greater Discourse on Ways of Undertaking Things (Mahādhammasamādāna-suttaṃ)</a></em> <sup>*</sup></li>
<li><a href="http://lirs.ru/lib/sutra/The_Middle_Length_Discourses(Majjhima_Nikaya),Nanamoli,Bodhi,1995.pdf#page=829" rel="nofollow noreferrer"><em>MN 101, To Devadaha (Devadaha-suttaṃ)</em></a>  </li>
</ul>

<p>* These discourses seem to answer the question directly.</p>
 43: <p>Devadaha Sutta (MN 101) linked to by @Yuttadhamo is the right sutra to consider, that fully covers this topic. As you can see in MN 101, the Jains too held position that "burning" past karma through exertion and austerity can lead to liberation.</p>

<p>As he interrogates Jains, Buddha makes following points:</p>

<ul>
<li>Not all pain comes from causes in the past. Some pain obviously comes from fierce striving, fierce exertion performed in the here-and-now. (As my first teacher used to say, sometimes pain comes from dental crowns and not from karma.)</li>
<li>Unfortunately, we can't really see how much negative karma we have accumulated, and how much karma has been exhausted so far.</li>
<li>If we saw that, then in theory we could talk about removing karma through exertion, similarly to how surgeon removes a poisoned arrow, producing pain short-term, but stopping it long-term.</li>
<li>Unfortunately, that is not possible, because: 
<ul>
<li>Unfruitted karma that is to fruit <em>in one way</em>, cannot be converted to fruit <em>in another way</em>, through striving &amp; exertion.</li>
<li>Unfruitted karma that is to fruit <em>in the future</em>, cannot be converted to fruit <em>in the present</em>, and vice versa, through striving &amp; exertion.</li>
<li>Unfruitted karma that is to bring result <em>of one size</em>, cannot be converted to bring result <em>of another size</em>, through striving &amp; exertion.</li>
</ul></li>
</ul>

<p>Instead, according to Buddha's teaching in MN 101, liberation from <code>dukkha</code> is achieved by <strong>"abandoning of unskillful mental qualities and the attainment of skillful mental qualities in the here-&amp;-now"</strong>.</p>

<p>Specifically, "skillful mental qualities" refer to 1) "exertion of fabrication against a cause of dukkha" which leads to "dispassion due to the fabrication", and to 2) "looking with equanimity at the cause of dukkha", which leads to "dispassion through the development of equanimity". In other words, cessation of <code>dukkha</code> is attained through 1) deliberate control of one's perspective, and through 2) equanimity that comes from philosophical attitude.</p>

<p>As an example of typical dukkha-pattern, Buddha tells a story of unshared love, with the protagonist suffering from "sorrow, lamentation, pain, distress, &amp; despair" due to being "in love with her, his mind ensnared with fierce desire, fierce passion". The protagonist then wilfully abandons "desire &amp; passion for that woman" (an effort that serves as "exertion of fabrication against a cause of dukkha") and as a result attains dispassion "due to the fabrication".</p>

<p>With all of the above in mind, Buddha still admits to importance of pushing oneself and overcoming one's limits -- to avoid regress due to indulgence -- but only inasmuch as to have "unskillful qualities decline" and "skillful qualities increase":</p>

<blockquote>
  <p>So he exerts himself with stress &amp; pain, and while he is exerting
  himself with stress &amp; pain, unskillful qualities decline in him, &amp;
  skillful qualities increase. Then at a later time he would no longer
  exert himself with stress &amp; pain. Why is that? Because he has attained
  the goal for which he was exerting himself with stress &amp; pain.</p>
</blockquote>

<p>As a result, </p>

<blockquote>
  <p>A monk, when not loaded down, does not load himself down with pain,
  nor does he reject pleasure that accords with the Dhamma, although he
  is not fixated on that pleasure.</p>
</blockquote>
 18: <p>I never really understood this view, but it seems to have been held by the Niganthas. See <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.101.than.html">MN 101</a> for a detailed argument against this sort of reasoning (too long to quote here).</p>

<p>Basically, though, it is like saying that if I have taken poison, I should take more poison so I feel the poisoning more quickly and thus somehow work out the result of the original poison quicker. Isn't that a ridiculous idea?</p>

<p>If I have performed karma X in the past that has result A in the future, performing other karmas Y and Z that also have result A doesn't do anything (except perhaps coincidentally - e.g. cutting off my arm means I can't experience pain in my hand) to affect karma X.</p>

<p>Another fallacy here is the idea that experiencing suffering leads to future happiness (in a way that pleasure doesn't). Really, to be objective, your question would have to include pleasure, in which case it would be, "If I undergo pleasure and pain in this life, will my next rebirth be better?" to which the answer is of course no. </p>

<p>An important concept to always keep in mind, according to the Buddha's teaching, is that <strong>pleasure and pain don't lead to pleasure or pain, it is good and evil that lead to pleasure and pain</strong>.</p>
