Paul McKeksdown,
The problem with your theory is that you don't see any limits. When Tzero is hotter, the T5 must go hotter for a given power, by about 3.5 degrees C per degree Tzero. That means the turbine temp limit is reached earlier, so the power output of the engine is strongly influenced by temperature. At constant pressure alt, the engine power drops off by about 1% power for each degree C Tzero rise. Big influence that temperature has. Big.