The invention relates to a cooling system (1) for a motor vehicle (3), comprising at least one heat exchanger (14, 15), in particular an intercooler, which is traversed by a medium, in particular a coolant that is used to cool a motor (9) and which comprises a heat exchanger air-penetration surface that is traversed by an air stream along a first stream path (26) in a first operating mode, in particular a back-pressure mode and is additionally or alternatively traversed by an air stream along a second stream path (24) running through an air conduction unit (20) in a second operating mode, in particular a ventilator mode. The air conduction unit is located between the heat exchanger (14, 15) and the motor (9) and comprises a conduction air-penetration surface. The aim of the invention is to provide a cooling system, in which the cooling air stream is obstructed as little as possible along the first stream path (26) in the first operating mode and which permits the cooling air stream to be conducted along the second stream path (24) with minimal loss. To achieve this, the air-conduction device (20) and the heat exchanger (14, 15) are configured and arranged in such a way that a parallel projection of the conduction air-penetration surface in the longitudinal direction (8) of the vehicle (3) on the plane containing the heat-exchanger air-penetration surface, protrudes at least partly beyond said heat-exchanger air-penetration surface and that a significant part of the heat-exchanger air-penetration surface is not covered by the parallel projection of the conduction air-penetration surface.