The invention discloses an air conditioning system of a motor vehicle and a method for operating the air conditioning system. The air conditioning system of a motor vehicle with a refrigerant circuit for operation in a refrigerator mode and a heat pump mode are provided. The refrigerant circuit includes a primary circuit with a compressor, a heat exchanger for heat transfer between the refrigerant and the surroundings, an expansion element and a heat exchanger for heat transfer from the intake air being conditioned for the passenger compartment to the refrigerant, and a first flow path. The first flow path extends from a branching point between the compressor and the heat exchanger to an opening and includes a heat exchanger for heat transfer from the refrigerant to the intake air being conditioned for the passenger compartment. The heat exchanger is situated in a flow direction of intake air of the passenger compartment after the heat exchanger 9. The air conditioning system is constituted with a heat exchanger for heat supply and acts as a part of the refrigerant circuit for heating input air to a passenger compartment. The heat exchanger for heat supply is disposed downstream the heat exchange along the input air to the passenger compartment. In addition, the invention discloses a method for operating the air conditioning system.