Warmer air, less dense. Less dense air means less mass flow of air through the combustion chamber, therefore less fuel can be burned, therefore less thrust. You could turn the compressors faster to recover air mass flow, but this would involve higher turbine temperatures, which are probably already limiting at take-off power. So accept the lower thrust.
Instead of turbine temperature, N1 or N2 might be limiting. Either way, you get the same result: warmer air --> less thrust.
Awaiting correction from those with more knowledge...