A Vuilleumier heat pump comprises a high temperature section and a low temperature section. The high temperature section includes a high temperature chamber heated by a combustion unit, and a high temperature heat exchanger. The low temperature heat section includes a low temperature chamber and a low temperature heat exchanger. During a room-cooling mode, the high and low temperature heat exchangers are connected to outdoor and indoor heat exchangers, respectively. During a room-heating mode, the high temperature heat exchanger is connected to the indoor heat exchanger, and the low temperature heat exchanger is connected to an auxiliary heat exchanger which transmits heat from the combustion unit to the low temperature heat exchanger.