This study aims to assess the effect of adding twisted fins in a triple-tube heat exchanger used for latent heat storage compared with using straight fins and no fins. In the proposed heat exchanger, phase change material (PCM) is placed between the middle annulus while hot water is passed in the inner tube and outer annulus in a counter-current direction, as a superior method to melt the PCM and store the thermal energy. The behavior of the system was assessed regarding the liquid fraction and temperature distributions as well as charging time and energy storage rate. The results indicate the advantages of adding twisted fins compared with those of using straight fins. The effect of several twisted fins was also studied to discover its effectiveness on the melting rate. The results demonstrate that deployment of four twisted fins reduced the melting time by 18% compared with using the same number of straight fins, and 25% compared with the no-fins case considering a similar PCM mass. Moreover, the melting time for the case of using four straight fins was 8.3% lower than that compared with the no-fins case. By raising the fins’ number from two to four and six, the heat storage rate rose 14.2% and 25.4%, respectively. This study presents the effects of novel configurations of fins in PCM-based thermal energy storage to deliver innovative products toward commercialization, which can be manufactured with additive manufacturing.