A gas turbine engine including a compressor rotor and a turbine rotor connected by a compressor shaft portion connected to the compressor rotor and a turbine shaft portion connected to the turbine rotor. The compressor shaft portion and the turbine shaft portion are connected axially together by a shaft coupling, between the compressor rotor and the turbine rotor, and at least a bearing rotatably coupled to the compressor shaft portion adjacent the shaft coupling. The compressor shaft and/or the turbine shaft are provided with openings permitting cooling air to enter air passages in the area of the shaft coupling and surrounding the end of the turbine shaft portion, in order to dissipate heat originating at the turbine rotor and thus reducing the thermal stresses at the bearing.