This article presents an example of the joint use of a compressor heat pump that uses propane as a natural, ecological thermodynamic medium and a phase heat accumulator that uses paraffin as a medium. Special attention has been paid to the solidification process of the phase change material, and a simple theoretical model of the solidification of this material has been proposed. Thermodynamic balance calculations were carried out for the compressor heat pump and the phase heat accumulator. This paper presents a theoretical analysis of two examples of heating using a compressor heat pump, implementing the Linde cycle for the refrigerant R290 (propane): high-temperature heating at a temperature of 80 °C and low-temperature (surface) heating at a temperature of 60 °C, with the same unit heat output of 0.376 kW taken from the lower-temperature heat source of each evaporator. This heat is generated by the solidification of the PCM. The compressor power is 77 W in the first case and 40 W in the second. The energy efficiency coefficients of the compressor heat pump for the proposed combination of a phase heat accumulator and compressor heat pump are 5.98 and 10.40. The joint use of a heat accumulator and a heat pump presented in this paper can be used in applications for the heating of domestic water or water for space heating.