A cooling system for cooling an electric machine of a motor vehicle, including a supply line, at least one cooling line, and a bypass line. The supply line is for supplying a cooled coolant to a first winding head region of the electric machine. The at least one cooling line leads from the first winding head region through a stator of the electric machine up to a second winding head region of the electric machine. The bypass line is guided from the first winding head region to the second winding head region past the stator. The bypass line, to collect and/or discharge air, exits from the first winding head region at a highest position in a direction of gravity and/or opens into the second winding head region at a highest position in the direction of gravity.