A pump has a suction region, a pressure region, and a pressure space which has an outflow region. A rotor is connected to a shaft in which rotor delivery elements are displacably received. The rotor has expelling regions connected to the pressure region by way of a first fluid path. A cold starting device is prestressed into a first functional position to shutoff a second fluid path from the pressure region to the pressure space, and is configured to be displaced counter to the prestress into a second functional position to open the second fluid path. The cold starting device is arranged in its second functional position at least in regions with a relief face which faces away from the pressure region in a relief receptacle. The relief face is loaded during operation of the pump with a pressure being smaller than a system pressure in the outflow region.