Air conditioning system of a motor-vehicle

In an air-conditioning system for motor vehicles, the radiator (2) for heating the passenger compartment (10) is excluded from connection to the circuit for cooling the engine when heating of the passenger compartment (10) is not required. In said condition, a mixing valve (M) that controls the flow of air (F) downstream of an evaporator (12) of the circuit for cooling the motor vehicle is set in an intermediate position, in which part of the flow of air leaving the evaporator (12) flows directly in the passenger compartment of the motor vehicle, keeping it cooled, whilst part of the flow of air leaving the evaporator (12) flows through the aforesaid heating radiator, which in said condition functions as accumulator of cold. In the steps in which the passenger compartment (10) must continue to be cooled but the cooling circuit is temporarily deactivated, for example on account of an arrest of the engine of the motor vehicle due to a strategy of the stop-and-start type, cooling of the passenger compartment is ensured by the aforesaid radiator (2) that in said step yields the cold previously accumulated to the flow of air that traverses it before reaching the passenger compartment (10).