A cooling system of an internal combustion engine of a motor vehicle has a cooling circuit, including a coolant/air radiator for cooling the engine, and a heating circuit, including a coolant/air heat exchanger for heating the passenger compartment. The cooling system includes an additional or secondary heater integrally associated with a coolant/air radiator to increase the heating capacity. The problem encountered with modern engines, particularly diesel engines, is that too little heat is available for heating the passenger compartment. Consequently, a secondary heater is needed. The secondary heater, which can be a fuel heater with a burner part and a heat exchanger part, is integrated into the radiator. This arrangement is advantageous in that the burner, with its fuel and exhaust gas line, is located outside the passenger compartment.