A cooling system has a drive motor which is to be cooled by a cooling medium. A cooling medium circuit conducts the cooling medium. A hydrodynamic machine comprising a working space can be filled with a working medium. The working medium is the cooling medium, and the hydrodynamic machine has a seal which is cooled and/or lubricated by the cooling medium. A cooling medium pump for circulating the cooling medium is in the cooling medium circuit. A pick-off is in the cooling medium circuit in the region of the cooling medium pump. Via the pick-off, the cooling medium is branched out of the cooling medium circuit. The branched-off cooling medium is conducted directly through or past the seal to cool and/or lubricate the latter, and the cooling medium which is conducted through or past the seal is supplied to the cooling medium circuit upstream or downstream of the working space.