The air conditioning system including at least one sensor of the thermal comfort of the passenger compartment of a motor vehicle, and an apparatus having at least one pair of heat-exchanger units, each designed to increase and reduce said temperature at alternating intervals under the control of the sensor. Each heat-exchanger unit comprises a substrate having the property of absorbing and releasing heat according to the absorption of a gas. The two substrates are set in two hermetic casings in communication with one another through a compressor and a series of valves, which can be actuated so as to transfer the gas alternately from one to another of the two substrates. Each heat exchanger unit also includes an outlet conveyor with an outlet opening to the passenger compartment and another outlet opening towards the outside. The two outlets are controlled by hatches that can be actuated intermittently so as to send hot air or cold air continuously into the passenger compartment.