Flow machine cooling

The machine has a rotor rotatably supported around a rotational axis. An inner housing is arranged around the rotor. A flow channel is arranged between the rotor and the inner housing. Another flow channel is formed in a flow direction (18) opposite to the former channel. A piston balancing line (13) supplies steam between the inner housing and a thrust balancing piston of the rotor. A piston balancing line surface is formed as enlarged opposite to a pipeline surface, and/or a piston balancing line inner surface (20) is formed as enlarged opposite to a pipeline inner surface (21).