Here we describe the results of a computational and experimental study investigating the effects of using paraffin wax as a low-cost phase change material (PCM) on the efficiency of heat exchange in a domestic water heating system. Our system comprises an annular heat exchanging element containing paraffin wax, and a columnar aluminum water reservoir inside. To assess performance, we circulated 80℃ water through the heat exchanger for different durations of time, and measured temperatures in the paraffin over the subsequent 14 hours as the system cooled. Experiments were repeated, and temperature decay measurements compared against a control condition in which no PCM was present. Additionally, we carried out numerical computational fluid dynamics (CFD) simulations to help characterize the melting dynamics, and predict temporal fluctuations in the PCM during experimental trials. While results from experimental trials suggest that the paraffin wax PCM was not significantly different from the control, CFD data implied that certain design modifications (such as the introduction of heat spreaders) might improve the performance of paraffin wax as a PCM in domestic and commercial water heating systems.