A compressor with a cylinder head (33, 29) comprises a lower cylinder head section (33) and an upper cylinder head section (29) connected to each other. A seal (12) is provided between the faces of the lower cylinder head section (33) and the upper cylinder head section (29) facing each other. A suction space (31, 25) and a pressure space (10, 17) as well as a suction valve (32, 4) and a pressure valve (5, 7) are installed in the cylinder head (33, 29). A compression space (3) of the compressor is connected by the suction valve (32, 4) to the suction space (31, 25), and by the pressure valve (5, 7) to the pressure space (10, 17). The suction space (31, 25) is also connected by a suction connection (71) to the atmosphere, and the pressure space (10, 17) is connected to a consumer by a pressure connection (18) to a source of pressure. In order to achieve efficient transfer of heat in the cylinder head (33, 29), a wall-like part (76), made of a material with good heat transferring properties, is provided at least in the pressure space (10, 17) to subdivide the pressure space (10, 17) of the cylinder head (33, 29) into a first pressure chamber (10) and a second pressure chamber (17). The first pressure chamber (10) and the second pressure chamber (17) are connected to each other by a passage opening (77) located in the wall-like part (76). Desirably, the suction space (31,15) is subdivided into first and second suction chambers (31,15) by a U-shaped part (79,80) having a second passage opening (78).