Henning, I am going to take a shot at this. A turbine is a normally aspirated engine. As the air thins the horse power decreases. On airframes with flat rated engines there is a limiting factor as to how much power is allowed to be used. Let me use approximate numbers for the Cheyenne IIIA since I am a little more familiar with it.
The airframe is limited to 720 HP per side. At sea level the engines are capable of much more than that with out damage to the gas generator. The restriction may be due to any one or combination of factors. Perhaps the gear box, maybe the prop itself. Could be the engine attachment or perhaps the size of the rudder. Maybe the factory does not want to exceed 720 per side in case of engine loss.
On take off we run the power up to the max torque which at take off prop RPM yields 720 HP. Your ITT will be below redline by quite a bit, depending on air density. If we do not touch the power levers the torque will drop along with fuel flow as we climb. Temps will remain mostly constant. At PERHAPS 10 maybe 12 thousand feet we will run out of climb.
In the real world after T O we continue to move the power levers forward to maintain torque. We can do this because we were only using partial power on T O. Those 720 HP engines are actually capable of making perhaps 900 HP at sea level. As we add fuel in the climb the turbine is generating more gas and turning the compressor faster producing more air flow. Part of the air being pushed through the compressor is used for cooling. In fact only the excess air is used for cooling. By cooling I am talking about the air used to shape the flame keeping it away from the burner can sides, and also the air going through the blades and vane rings. They are hollow to allow airflow for cooling.
As you climb you have less and less excess air. At some point you do not have enough excess air to maintain the ITT below the red line which makes you temped out and you will no longer be able to make 720 HP above that altitude.
I do not know all of the magic of the Fuel Control Unit but it senses among other things P1 and P2 pressure to know how much air is available for burning kerosene and reacts accordingly. The thing that MIGHT be tripping you up is this lack of air, increasing temp. It is not a lean rich thing. The air to fuel ratio remains constant and the pilot has no control of that. The increase in temp is strictly a function of available excess air for cooling. ITT is not the temperature of the flame but rather the various parts of the gas generator. Thus Wayne is correct in that the engine is in a way air limited. Once you don't have enough air for cooling then that is it.
That is the way flat rating is used to increase cruise speed. You use the excess HP you have on the ground to maintain the flat rated HP to a higher altitude.
Hope this makes some sense.
