By placing multiple Peltier elements in a linear arrangement while two water flows run past the elements, a temperature increase can be realised in one flow while the other flow is cooled down. In this study the heating of domestic hot water with Peltier elements as solid state heat pumps, and a heating network was investigated. A numerical model that solves the thermal energy balance within the Peltier elements was derived to describe the internal temperature distribution of the Peltier element, and its interaction with the domestic hot water and the heating network. The model was used to simulate the performance of 40 Peltier elements in a custom designed Peltier Heat Exchanger. Experiments were run to validate the numerical model. The numerical simulation of the temperature distribution within a Peltier Heat Exchanger and the temperature distributions observed in the experiments were not in agreement. The model input parameters Seebeck coefficient, resistance, thermal conductivity and a relation for the Nusselt number were re-evaluated using the experimental results. After the adjustment of the model input parameters, the new simulation results were able to accurately describe the temperature distribution with the Peltier Heat Exchanger. The Peltier Heat Exchanger was able to deliver domestic hot water with a COP between 1.2 and 1.8 depending on the flow speed of the domestic hot water and the heating network. The COP can potentially be increased by using Peltier elements with a higher Seebeck coefficient.