An apparatus and method of cooling a gas turbine engine 10 including a core 44 with a compressor section 22 in which the compressor section 22 includes a closed loop cooling circuit 84 having a pump 86. A heat pipe 94 extends from a stationary vane 60, 62, a heat exchanger 76 is located within the bypass air flow 47, and a coolant conduit 90 passes fluidly coupled to the pump 86 and heat exchanger 76 and passing by the heat pipe 94. The pump 86 circulates coolant 98, 100, 114 to draw heat from the heat pipes 94 into the coolant 98, 100, 114. The heated coolant 100 then passes through the heat exchanger 76, where the heat is rejected to the bypass air 47 to cool the coolant 98, 100, 114 to form cooled coolant 98, which is then returned to the heat pipes 94.
