Abstract: A cooling and heating system includes a hot water tank having a hot water heat exchanger, an indoor heat exchanging assembly including first and second indoor heat exchangers, an outdoor heat exchanger, and a vuilleumier heat pump. Fluid medium from a high temperature side of the heat pump is circulated to the hot water heat exchanger in both the heating and cooling modes. In the heating mode, fluid medium exiting the hot water heat exchanger travels through the first indoor heat exchanger. In the cooling mode, fluid medium is circulated through the hot water heat exchanger and then back to the heat pump while simultaneously fluid medium from the low temperature side of the heat pump is circulated through the second indoor heat exchanger. During a hot water heating mode, fluid medium from the high temperature side of the heat pump is circulated through the hot water heat exchanger without being circulated through the indoor heat exchanging assembly.