The utilization of low-temperature waste heat, particularly from electrolyzers, in district heating networks via heat pumps presents a promising approach to accelerate the decarbonization of the heat sector. However, managing the electrolyzer’s specific temperature requirements and dynamic waste heat output, while simultaneously meeting the district heating network’s variable temperature demands, requires the implementation of an advanced control system for the heat pump cycle. For this, model predictive control is a promising approach since it not only ensures the satisfaction of constraints, but also facilitates a direct optimization of the heat pump’s operational efficiency. Nevertheless, model predictive control requires a dynamic heat pump model. In this context, first-principles models are often used. However, they are very complex and difficult to parameterize for real heat pumps. Therefore, in the present paper, a data-based system identification is carried out to obtain a reduced-order heat pump model from a high-fidelity first-principles simulation model. Based on the identified model, a predictive controller is implemented. The effectiveness of the obtained controller for operating the first-principles model is demonstrated in a numerical case study.