Multi-function heat pumps able to recover the condensation heat to prepare domestic hot water (DHW) while simultaneously satisfying the cooling energy needs are a suitable solution to reduce the overall energy demand of buildings during the summer season. In this work, the seasonal energy performance of an air-to-water heat pump with condensation heat recovery was investigated numerically. A large multi-storey building, partially renovated recently, was considered a case study. A numerical model integrating the building and the HVAC system was implemented with the dynamic software TRNSYS 18. To evaluate the influence of climatic conditions on the system performance, the building energy demand for space cooling and DHW preparation was calculated for five locations in the North and South of Italy, characterized by different climates. The seasonal performance factor of the multi-function heat pump was assessed numerically and compared to that of a conventional reversible heat pump not able to recover the condensation heat. The numerical results show that adopting a multi-function heat pump improves the system SPF by up to 15% compared to a conventional heat pump, since up to 60% of the DHW energy demand can be covered in heat recovery mode. The paper also shows that the climate significantly influences the system seasonal efficiency. In locations characterized by a hot summer, the cooling and DHW loads are simultaneous for a large share of the season, and, therefore, the recovery of condensation heat can be maximized.