A thermal machine includes a hot gas channel; a shell bounding the hot gas channel; a cooling shirt surrounding the shell; and a cooling channel disposed between the shell and the cooling shirt and configured to convection cool the hot gas channel with a cooling medium, wherein the cooling shirt includes at least one local divergence in the guidance of the cooling medium so as to compensate for non-uniformities in at least one of a thermal load on the shell and a flow of the cooling medium in the cooling channel.