A reciprocating piston machine for compressing a fluid, more particularly ambient air, for a compressed air system of a motor vehicle, includes a cylinder housing and a cylinder head constructed layer by layer and including a valve carrier element with an outlet valve, a chamber plate and a head plate with a pressure medium outlet. A cooling medium channel for cooling at least a partial region of the cylinder head and an outlet channel for connecting the outlet valve to the pressure medium outlet are provided and extend through components of the cylinder head, at least in portions. In order to improve the cooling, at least a partial portion of the cooling medium channel and a partial portion of the outlet channel are allocated to the cylinder housing.