An inop APU should not have any impact on the EGT of the engines. Not during T/O or any other condition.
The 75īs usually have a 5- or 10 minute T/O thrust limit. By that time you should have passed 400', so if it is required to select climb thrust before that height, something is deeply wrong with the engines.
During normal operations APU is shut down prior to T/O, so again taking off should never be a problem on that aircraft with a APU inop. But if you have to select climb thrust before 400', then you have a problem.
Rgds-