A cooling system for a motor vehicle includes a first cooling circuit through which a coolant can flow, and at least one drive machine by means of which the motor vehicle can be driven, disposed in the first cooling circuit and thus is cooled by means of the coolant. A first cooler for cooling the coolant flowing through the first cooling circuit is disposed in the first cooling circuit. The system further includes a second cooling circuit through which the coolant can flow, and a flow branch, through which the coolant can flow and in which a second cooler is disposed for cooling the coolant flowing through the flow branch. A valve device can be switched between a first switching state and a second switching state to thereby connect the second cooler selectively, and thus as required, to the first cooling circuit or to the second cooling circuit.