In recent years, due to the global energy crisis, the idea of a photovoltaic-assisted air-source heat pump (PV-ASHP) has become increasingly popular. This study provides a simulation in TRNSYS and the analysis of the use of a PV-ASHP system in a service building in different climate zones of Poland. For each of the six cities—Kolobrzeg, Poznan, Krakow, Warsaw, Mikolajki, and Suwalki, the effect of changing five system parameters (area, efficiency, type, and location of photovoltaic panels, and the use of a heat pump control strategy) on the amount of energy generated and consumed was determined. We also estimated the extent to which the photovoltaic panels could cover the energy requirements for the heat pump (HP) operation and the system could provide thermal comfort in the service room. Finally, a simplified analysis of the operating costs and capital expenditures was made. The results highlighted the issue of the incoherence of renewable energy sources and the need to store surplus energy under Polish climatic conditions. Abandoning the HP control strategy increased energy consumption by 36–62%, depending on the location and Variant, while the change in the place of the PV panels on the roof slope reduced energy generation by 16–22%. When applied to an ASHP in a service building, the use of PV panels to power it seems to be cost-effective.