Abstract: A cooling system for stationary vanes in the turbine section of a gas ture. Combustors for the turbine are disposed in a chamber that receives compressed air from a compressor section. This compressed air forms both combustion air and cooling air. The cooling air portion of the compressed air is recirculated through the vanes by bleeding it from the chamber and further pressurizing it, after which it flows through a cooling air flow path in the vanes, thereby resulting in the cooling of the vanes and the heating of the air. The heated air is then returned to the chamber where it mixes with the incoming combustion air, thereby giving up a portion of the heat transferred from the vane to the combustion air. As a result, the temperature of the combustion air is increased, thereby increasing the thermodynamic efficiency of the gas turbine.