The engine power rate is related always to the ISA temperature. Temperatures below ISA will give you max power. From ISA to ISA+40º engine performances are gradually degraded because of EGT limits, that is to say "You can not use full power" then you use reduced or derated power always function of the EGT MAX.
Considere the same air mass. As its temperature increases you may add less temperature (=fuel burned) to reach max EGT.
Aerodynamics works the same with ISA. So, when you TO below ISA to ISA you can always use full TO power and have more lift, resulting on LESS RWY needed for a given TO weight. If you adjust your performances to the full lenght of the RWY and the obstacles at the TO path then you will use less power, less EGT and more rwy.