An air conditioning system (10) for the passenger compartment of a motor vehicle comprising a main tube (22) for fluidly connecting a compressor (12) to an outside heat exchanger (14), the outside heat exchanger to an expansion device (16), the expansion device to an inside heat exchanger (18), the inside heat exchanger to an accumulator (20), and the accumulator to the compressor; a bypass tube (28) fluidly connected to the main tube between the compressor and the outside heat exchanger and between the expansion device and the inside heat exchanger; and a valve (30) positioned in the bypass tube; wherein the valve has a closed position when refrigerant fluid flows through the main tube in a first direction (X) from the compressor through the outside heat exchanger, the expansion device, the inside heat exchanger and the accumulator back to the compressor, for cooling of the passenger compartment, and an open position when refrigerant fluid flows in the first direction and through the bypass tube and the valve for heating of the passenger compartment. Provides supplemental heating without using a calibrated expansion device.