A compressor module for compressing gas composed of a compressor element with a housing with integrated compressor element cooler; a motor and a gas cooler for cooling the compressed gas originating from the compressor element. The gas cooler includes a primary section through which the gas to be cooled can be guided and a secondary section that is in heat-exchanging contact with the primary section. A first cooling circuit can guide a coolant through the secondary section of the gas cooler or through a section thereof and a second cooling circuit can guide a coolant through the compressor element cooler. The first cooling circuit and the second cooling circuit are joined together in series or in parallel and are guided to a common output.