Cooling device for cooling a high-pressure exhaust-gas recirculation loop of a motor vehicle engine, comprising a first heat exchanger in heat-exchange relationship with the cooling circuit of the engine, a bypass of the first heat exchanger, and a control module able to actuate a bypass valve in an "active bypass mode 1" or "inactive bypass mode 1", and to actuate another bypass valve in an "active bypass mode 2" and "inactive bypass mode 2", the control module being capable of actuating the bypass of the first heat exchanger via the bypass valve in the "active bypass mode 1", the cooling device comprising a second heat exchanger in heat-exchange relationship with a cooling circuit independent of the cooling circuit of the engine, the second heat exchanger being mounted in series in the recirculated-gas flow with respect to the first heat exchanger, the cooling device comprising a bypass of the second heat exchanger, the control module being capable of actuating the bypass of the second heat exchanger via the bypass valve in an "active bypass mode 2", the cooling device comprising a recirculation valve, characterized in that the valve is mounted on the recirculation duct, between the first and second heat exchangers (32, 40), the recirculation valve being placed between the bypasses (34, 42), and in that the control module comprises temperature sensors (60, 74, 87) able to respectively measure the temperature (T F1) of the fluid circulating in the cooling circuit of the engine, the temperature (T F2) of the cooling fluid circulating in the second cooling circuit, and the outside air temperature (T EXT), and comparators (92, 94 and 96) respectively intended to compare a temperature (T F1, T F2, T EXT) with a reference temperature (T F1_REF, T F2_REF, T EXT_REF) which is specific thereto, the control module being able to determine an opening setpoint of the recirculation valve in accordance with various parameters, and is parametrized to carry out, in this order: - the control module comprises a detector of the rotational speed (Reg) of the engine, a detector of the load (Chg) of the engine and a computer capable of calculating the operating point of the engine of the vehicle in accordance with the data (Reg, Chg) respectively measured by the detectors of the engine rotational speed and load (Reg, Chg) and of comparing said operating point with a reference operating point, said control module being parametrized to inhibit the actuation of the bypasses (34, 42) of the first heat exchanger and of the second heat exchanger when the operating point exceeds the reference operating point, - a measurement of the temperature (T EXT) of the outside air, - a comparison of the temperature (T EXT) of the outside air with a reference datum (T EXT_REF) such that, if the temperature (T EXT) of the outside air is above the reference datum (T EXT_REF), then - a measurement of the temperature (T F1) of the fluid circulating in the cooling circuit of the engine is carried out, then - a comparison of said measured datum (T F1) with a reference datum (T F1_REF), and - an actuation of the bypass of the first heat exchanger as long as the temperature (T F1) is below the reference datum (T F1_REF), - a measurement of the temperature (T F2) of the cooling fluid circulating in the second cooling circuit when the temperature (T F1) is above the reference datum (T F1_REF), - an actuation of the bypass of the second heat exchanger as long as the temperature (T F2) of the cooling fluid is below a second reference cooling fluid temperature (T F2_REF), the engine control device actuating the bypass valve in the "inactive bypass mode 1", the bypass valve remaining in the "active bypass mode 2". - the control module comprises a detector of the rotational speed (Reg) of the engine, a detector of the load (Chg) of the engine and a computer capable of calculating the operating point of the engine of the vehicle in accordance with the data (Reg, Chg) respectively measured by the detectors of the engine rotational speed and load (Reg, Chg) and of comparing said operating point with a reference operating point, said control module being parametrized to inhibit the actuation of the bypasses (34, 42) of the first heat exchanger and of the second heat exchanger when the operating point exceeds the reference operating point, - a measurement of the temperature (T EXT) of the outside air, - a comparison of the temperature (T EXT) of the outside air with a reference datum (T EXT_REF) such that, if the temperature (T EXT) of the outside air is above the reference datum (T EXT_REF), then - a measurement of the temperature (T F1) of the fluid circulating in the cooling circuit of the engine is carried out, then - a comparison of said measured datum (T F1) with a reference datum (T F1_REF), and - an actuation of the bypass of the first heat exchanger as long as the temperature (T F1) is below the reference datum (T F1_REF), - a measurement of the temperature (T F2) of the cooling fluid circulating in the second cooling circuit when the temperature (T F1) is above the reference datum (T F1_REF), - an actuation of the bypass of the second heat exchanger as long as the temperature (T F2) of the cooling fluid is below a second reference cooling fluid temperature (T F2_REF), the engine control device actuating the bypass valve in the "inactive bypass mode 1", the bypass valve remaining in the "active bypass mode 2".