Cooled cooling air system for a turbofan engine

A gas turbine engine comprising:

• a fan bypass duct defined between a fan nacelle and core cowl of an engine core;
• the engine core including a cooled cooling air system configured to receive cooling air from a primary flowpath bleed within the engine core and configured to provide cooled cooling air to at least one component within the engine core, the cooled cooling air system further including a cold air modulator having a first position, a second position, and at least one intermediate position between the first and second positions;
• the cooled cooling air system including an air-air heat exchanger;
• and
• a controller controllably connected to the cold air modulator and configured to control a position of said cold air modulator based on at least one of an engine power and a combination of engine rotor speed and ambient temperatureengine operating condition.