A gas turbine having a rotor which includes a turbine rotor, a shaft and a compressor rotor, the turbine rotor having at least one rotor disk and a rotor cone leading from the or a rotor disk to the shaft, the downstream end of the shaft being rotatably supported in a bearing having a bearing chamber, the interior space of the shaft being designed as a flow channel for bearing-chamber sealing air, and the space surrounding the rotor cone upstream of the same being designed as a flow space for cooling air is disclosed. In the region of the rotor connection, the shaft exhibits an expanded portion, at whose upstream end, openings are provided to allow cooling air to enter, and, at whose downstream end, openings are provided to allow cooling air to exit into the space between the bearing chamber and the rotor cone, a wall separating the streams of the cooling air and of the sealing air in the shaft interior from one another.