An apparatus and method of cooling a gas turbine engine including a core with a compressor section in which the compressor section includes a closed loop cooling circuit having a pump, at least one heat pipe extending from at least one of the stationary vanes, a heat exchanger located within the bypass air flow, and a coolant conduit passing fluidly coupled to the pump and heat exchanger and passing by the heat pipe. The pump pumps coolant through the coolant conduit to draw heat from the heat pipes into the coolant to form heated coolant, the heated coolant then passes through the heat exchanger, where the heat is rejected from the coolant to the bypass air to cool the coolant to form cooled coolant, which is then returned to the heat pipes.