A cooling system with a circulating coolant for cooling a combustion engine in a vehicle (1) includes a first radiator (13), a first line circuit (14, 15, 16) which leads coolant from the first radiator (13) to the engine (2); a second line circuit (17, 18) which leads coolant from the engine (2) to the first radiator (13); a second radiator (20) upstream of the first radiator (13) in air flow through radiators; a third line circuit (21, 22, 24) including at least one line (21, 24) to lead coolant from a line (16) in the first line circuit to the second radiator (20), and a fourth line circuit (25, 26a-d, 27) which leads coolant from the second radiator (20) to the first line circuit (15) and which contains at least one cooler (29, 30, 31) for cooling a medium or component of the vehicle (1).