I'm astoundingly rusty on the maths, but in simplistic terms I think it works like this:
- Gas Turbine engine generates thrust through expansion of hot gases
- Greater the expansion, the greater the propulsive efficiency
- Hotter the gas, the more it's expanded (or will, particularly overall on mixing with bypass air)
- The hotter the gas, the higher the turbine temperature.
- Therefore higher turbine temp = higher efficiency.
To some extent also a higher temperature implies a maximum efficiency / stoichiometric fuel/air mix in the combustion chamber, so less unburned fuel is leaving the engine, which will also increase efficiency.
A crude explanation, lacking any maths or real engine theory, but about right I think.
G