An air conditioning unit is disclosed for motor vehicles. The air conditioning unit includes with a compression refrigerant circuit where a refrigerant circulates, comprising comprehensively switched in series with respect to fluid flow at least one compressor upstream of a heat-delivering heat exchanger, and an expansion element upstream of a heat-absorbing heat exchanger, whereby into the flow path leading from the outlet of the heat-delivering heat exchanger to the expansion element an additional heat exchanger is integrated thermally coupled to at least one cooling means the temperature of which can be put to values below the temperature of the refrigerant in the compression refrigeration circuit at the position of the refrigerant's outflow from the heat-delivering heat exchanger, and a method for its operation.