A gas turbine engine has a core engine with a compressor section and a turbine section. The compressor section includes a low pressure compressor and a high pressure compressor. A cooling air system taps compressed air and passes the compressed air through a heat exchanger. Cooling air passes over the heat exchanger to cool the compressed air, which is returned to the core engine to provide a cooling function. The heat exchanger is mounted through a flexible mount allowing movement between a static structure and the heat exchanger.