Methods and systems for operating an engine are provided. An engine core temperature is monitored. When the engine core temperature is below an engine thermal limit adjusted for a level of deterioration of the engine, an output power of the engine is set in accordance with a reference power based on non-thermal limits of the engine. When the engine core temperature is near or above the engine thermal limit adjusted for the level of deterioration of the engine, the output power of the engine is set to a value lower than the reference power based on non-thermal limits of the engine to reduce the engine core temperature.