How to reply to students' emails that show anger about their mark? I always find myself in a difficult situation on the rage of students who are upset about their marks they just received. I feel it is kind of difficult to reply to students' emails that sound very angry. Especially when they first receive their marks.

Why did I get this MARK!
How could I get this mark, when my colleague got higher!
I will provide my mark to the dean! (some already done so!)

I know that this is not uncommon, but I feel we have the duty to know how to deal psychologically with this behaviour.
How do you deal with this situation?
Some say, do not reply to this email before at least a week so that the student acknowledges and time for them to relax.
The issue is that I will have to deal with these same students in a module next term and I am worried about how they will portray me.
When dealing with angry students, your number one priority should be to de-escalate the situation and bring it back to a more factual ground. That means you want to:

Stay calm. Even if you are getting agitated yourself, you should never let it show through in your answer (easier via email than personally, but the same principle applies independently of the medium). I tend to opt for a more formal tone than what I usually use, mostly because I have found more formal phrasing harder to be misunderstood as dismissive (your milage may vary).
Provide short, to the point, answers. Answer the student's query or complaint politely, but don't get pre-emptively defensive and don't overly detailedly explain your reasoning. The more you write or say, the more an unhappy student will find to be upset about. There is a time and place to give a student detailed feedback, but when they are currently raging isn't it.
Stay with the facts. Scrub all subjectivity from your own answer. You want to bring the conversation to a place where you are talking about specific assessment results (exam questions, assignment tasks, etc.) rather than &quot;I felt I did better&quot;, and the more you are using subjective statements in your own answer the more the student will feel validated that his own subjective understanding of the situation is as valid as yours.
Require the student to provide concrete, factual arguments. Once you bring the discussion to a more factual level, you should ask the student why, specifically, they disagree with their grade. Are there specific assessment results they feel were wrongly graded? Are they unhappy with how you aggregated the assessments? Once you are discussing on this level, it becomes easier to both, convince a student that their grade is correct according to the framework, and see cases where your framework is indeed unfair (or can at least be perceived as such).
Answer, but don't answer too quickly. Especially when receiving complaints via email: avoid the temptation to immediately answer questions by upset students. Give it a day, this will allow both you and the student a chance to calm down. A little delay in your interaction will also motivate the student to think more carefully about what they are actually writing, since a non-question like &quot;How could I get this mark, when my colleague got higher&quot; just means longer delay for them.
Remember that student's don't have to agree with their grade. At the end of the day, not all students will be happy with their grade, and even after you have explained your reasoning not all students will be convinced. That's ok. You and the student don't have to agree on the final grade. There is a process in place what, if anything, students can do to further escalate a grade dispute (I don't know if that includes sending a mail to the dean at your department, in mine emailing the dean about a grade dispute would mostly result in a confused dean).