A cooling device for an energy conversion apparatus having an electric machine, comprising a rotor mounted to rotate around an axis of rotation, which rotor is arranged on a rotatable central shaft, and having at least one first turbine, which is arranged rotatable on the same shaft, is specified. The cooling device comprises at least one first inner cavity of the shaft for transporting the coolant to a region inside the rotor, wherein the first inner cavity extends axially through the first turbine and through an axial space between the first turbine and the rotor. Also specified is such an energy conversion apparatus having such a cooling system. Finally, a cooling method for cooling such an apparatus having such a cooling system is specified.