Abstract: A motor vehicle has a low exhaust heat engine (ME) for driving the driven wheels and a system for conditioning the air temperature of the passenger compartment (CAB). The conditioning system includes a reversible heat pump (PAC) which conditions in temperature respectively a distribution loop (DI) and an exhaust loop (RE) through which flows a coolant. The distribution loop (DI) is connected to an exchanger (H2) with the air entering the space compartment (CAB) and is connectable via an electromagnetic valve (EV1) to another exchanger (H1) with the air entering the passenger compartment (CAB). The exhaust loop (RE) is connected to an exchanger (F1) with the outside air. The exhaust loop being further connected to the engine (ME) for exchanging heat with the engine.