A device for air-conditioning a motor vehicle has an engine-cooling loop, a heat-pump loop containing a compressor, an evaporator as cold source of the heat pump and a condenser as hot source of the heat pump. The condenser is integrated into the engine-cooling loop upstream of the air heater. An air-conditioning branch has a condenser and an evaporator with an upstream end connected to the heat-pump loop downstream of the compressor, and a downstream end connected to the heat-pump loop upstream of the compressor. Switching means make it possible to make the refrigerant fluid circulate either in the heat-pump loop, or in the heat-pump branch, in such a way as to form a heat-pump loop.