In the higher power regime, a gas turbine runs hotter at higher rpm because of the temperature "extracted" in the turbine to turn the compressor, which itself is delivering hotter air (adiabatic heating) to the burner.
But slowly accelerating out of idle, it's common to see the temp. cooler at 80% e.g. than at 65%. This is because the efficiency is falling off at lower rpm. Thus there is usually a "bucket" or "sweet spot" at part power where the turbine temp. is coolest.
