Heating and cooling of buildings account for around 15% of all global energy consumption. In light of the ongoing energy transition, we aim to improve the efficiency of both in a European single-family house by using photovoltaic-thermal collectors with a reversible heat pump for nocturnal radiative cooling, solar-assisted heating and domestic hot water generation. Two data-driven model predictive controllers activate the system during the most favorable ambient conditions for minimal energy consumption. Significant improvements in energy-efficiency of 39.0% for cooling, 21.7% for heating and 27.4% for domestic hot water are achieved over a simulation period of one year, compared to a conventional reference system. We find the building's underfloor radiant slab to be sufficient as a thermal storage for heating and cooling, not requiring a dedicated storage tank. However, a cost estimate indicates long amortization times for the higher installation costs of our proposed multi-energy system. Only the scenario with low-end estimates for the installation costs and high-end estimates for the electricity tariffs reached our target value of less than 20 years.