Obviously your ATPL courses does not cover the subject of jet engines extensively enough.
Just ask yourself what happens to the pressures/ temp in your engine as you accellerate down the runway with constant N1 and you have your answer.
However the fact that you did notice this is interesting, EGT is to the jest engine what body temp is to the human, higher that normal is a sign of.......
The key thing is to take note of the margin you have over the max EGT you will then have a good idea when you are going to make a critical Take Off as far as EGT is concerned.
With a bit of experiance you will be able to predict your peak EGT during Take Off as a function of OAT.
Part of our job is to know what is normal in order to detect early enough wat isn't.