The application describes a method of operating a gas turbine during a cool-down phase. The gas turbine provides a compressor, a combustor downstream of the compressor, and a turbine downstream of the combustor, with the turbine providing a turbine vane carrier. The method includes feeding a flow of cooling air from the compressor to the turbine vane carrier, measuring a temperature of the flow of cooling air and measuring a temperature of the turbine vane carrier. In the method, the flow of cooling air is fed at a first flow rate when the temperature of the turbine vane carrier is lower than the temperature of the cooling air, and the flow of cooling air is fed at a second flow rate when the temperature of the turbine vane carrier is higher than the temperature of the cooling air, wherein the first flow rate is higher than the second flow rate.