Is it appropriate to ask a professor to bump up a grade when I suspect it may be at the cutoff? Background: My course has three exams: I did really bad on the first, great on the second (97%), and I think well on the third. I regularly attended the professor's office hours and never missed class. 

Question: I now estimate that my final grade could be at the cutoff. Is it appropriate for me ask if he can round up grades (or bump up..) now before the grade is out? Or after the grade is out..?

Details: 

This professor didn't send out scores online for the previous two exams. He only allowed us to pick up the exam on the class. However, since everyone will be leaving, I don't know whether he is going to distribute the exam grade online or he is just going straight to put the final letter grade in the system. So, another option would be to e-mail him now and ask how he plans to distribute the exam grades.
Consider asking for an appointment to review the final exam.

Preemptively saying "I might be below the cut-off and would appreciate free points" is obnoxious. It's likely the professor has already taken your improvement and other factors into account. Further, asking for additional points for any reason other than a grading mistake is really inappropriate, though it's so common that most professors accept it. 

On the other hand, waiting until the final grades might be too long. Once the professor has made a decision about what grade you deserve, they are much less likely to reverse that decision. 

So, a good middle ground is to ask for an appointment to review the exam. This is a good thing to do in any case; further, the professor will take extra care when assigning your grade, as he will anticipate having to justify it to you. This also does not put you in an awkward position if you actually earned the grade you wanted -- you can just review the exam and thank him for a good course. Note, if you do this, you should make a good-faith review of the exam and an honest assessment of what you deserve; this is not "one weird trick" to get free points.