In order to enhance the heat transfer performance of a phase change thermal energy storage unit, the effects of trapezoidal fins of different sizes and arrangement modes were studied by numerical simulation in the heat storage and release processes. The optimal enhancement solution was obtained by comparing the temperature distribution, instantaneous liquid-phase ratio, solid–liquid phase diagram and comprehensive heat storage and release performance of the thermal energy storage unit under different fin sizes. During the heat storage process, the results show that when the ratio of the length of the upper and lower base of the trapezoid h1/h2 is 1:9, the heat storage time is shortened by 9.03% and 18.21% compared with h1/h2 = 3:7 and 5:5, respectively. During the heat release process, the optimal heat transfer effect is achieved when h1/h2 = 5:5. To further improve the heat transfer effects, the energy storage unit is placed upside down; then, the least time is achieved when h1/h2 = 2:8. When heat storage and release are considered together, the energy storage unit with h1/h2 = 2:8 takes the shortest time to melt in upright placement and then to solidify in upside-down placement.