A method is disclosed for cooling a gas turbine having a turbine, wherein a rotor, which rotates about a machine axis, carries a plurality of rotating blades, which are mounted by blade roots and extend with their airfoils into a hot gas path of the gas turbine. The rotor is concentrically surrounded by a turbine vane carrier carrying a plurality of stationary vanes, whereby the rotating blades and the stationary vanes are arranged in alternating rows in axial direction. An extended lifetime with external cooling is achieved by providing first and second cooling systems for the turbine.