This paper presents a distributed mathematical model for a carbon dioxide direct expansion solar-assisted heat pump used to heat bath water. The main components are a gas cooler, a needle valve, an evaporator/collector, and a compressor. To develop the heat exchange models, mass, energy, and momentum balances were used. The model was validated for transient as well as steady state conditions using experimental data. A reasonably good agreement was observed between the predicted temperatures and experimental data. The simulations showed that the time step required to demonstrate the behavior of the heat pump in the transient regime is greater than the time step required for the steady state. The results obtained with the mathematical model revealed that a reduction in the water mass flow rate results in an increase in the water outlet temperature. In addition, when the carbon dioxide mass flow rate is reduced, the compressor inlet and outlet temperatures increase as well as the water outlet temperature.