Originally Posted by
Dave Therhino
Tdracer may be able to offer more as turbine engine control system integration with aircraft is his area of expertise.
Sorry, a bit late to the party here (I was off line over the weekend and just catching up). I think the previous replies have covered it rather well - but in a nutshell once you get to the corner point temperature, the intent is to hold the burner exit/turbine inlet temperature constant and the max rated thrust (N1/EPR) is reduced as necessary to maintain the turbine inlet temp as the outside temperature increases.
Sometimes other factors come into play - e.g. max rotor speed margins - but as a general rule it's EGT which relates directly to the turbine inlet temp.