Air conditioning system for a vehicle and process for controling one air conditioning system for a vehicle

Temperature control system (10) comprises an evaporator (36) of an air-conditioning system through which heat and/or moisture are removed from air entering the vehicle interior, a first heat-exchanger arrangement (42) in the air flow direction downstream of the evaporator which supplies heat to the air, and a heating arrangement (20) with a second heat exchanger arrangement (22) in the air flow direction upstream of the evaporator. The second heat exchanger supplies heat to the air. An independent claim is also included for a process for operating the above temperature control system. Preferred Features: The heating arrangement is a fuel-operated heating device.