The utilization of latent heat thermal energy storage (LHTES) using phase change materials (PCM) has attracted considerable attention due to their high energy density and thermal regulation. However, the inferior thermal conductivity of PCM has hindered their widespread implementation, triply periodic minimal surface (TPMS) structures could considerably ameliorate the energy storage utilization. TPMS structures offer escalated surface area and pore interconnectivity, which can enhance the apparent thermal conductivity and improve the performance of LHTES systems. This study focuses on investigating the performance and storage capabilities of three unique TPMS structures, namely Gyroid, IWP, and Primitive, at different relative densities and charging temperatures. The computational model is developed, verified, and validated with the relevant experiment results. A comparative analysis of the temperature distribution and liquid fraction evolution in TPMS LHTES units is carried out and compared to pure PCM LHTES. At a charging temperature of 80 °C, compared to the complete melting time of 7206 s for the pure PCM LHTES, the results demonstrate that the G10, IWP10, and P10-PCM LHTES achieve complete melting at 344 s, 276 s, and 368 s, respectively. This affirms the superiority of IWP structures in improving the melting rates due to their escalated surface areas and tortuous paths. The use of TPMS structures improves the total heat storage, heat storage rate, and volumetric heat storage density, while reducing the gravimetric heat storage density, compared to the pure PCM LHTES. The G10-PCM LHTES attains total heat storage, heat storage rate, volumetric, and gravimetric heat storage density of 2120 J, 6.16 W, 63.6 kWh/m3, and 227 kJ/kg, compared to 1910 J, 0.27 W, 57.3 kWh/m3, and 250 kJ/kg for pure PCM LHTES, respectively. Moreover, increasing the relative density of TPMS structures adversely reduces the total heat storage, heat storage rate, and volumetric heat storage density, and significantly increases the heat storage rates. As the charging temperature increases, the complete melting time is reduced and the charging performance indicators are improved, for the pure PCM and TPMS-PCM LHTES units.