This study aims to develop a controller to operate an energy system-consisting of a photovoltaic thermal (PVT) system combined with a heat pump, using the reinforcement learning approach to minimize the operating costs of the system. For this, the flow rate of the cooling fluid pumped through the PVT system is controlled. This flow rate determines the temperature increase of the cooling fluid while reducing the temperature of the PVT system. The heated-up cooling fluid is used to improve the heat pump’s coefficient of performance (COP). For optimizing the operation costs of such a system, first an extensive simulation model has been developed. Based on this technical model, a controller has been developed using the reinforcement learning approach to allow for a cost-efficient control of the flow rate. The results show that a successfully trained control unit based on the reinforcement learning approach can reduce the operating costs with an independent validation dataset. For the case study presented here, based on the implemented methodological approach, including hyperparameter optimization, the operating costs of the investigated energy system can be reduced by more than 4% in the training dataset and by close to 3% in the validation dataset.