The design of the latent heat thermal storage system (LHTESS) was developed with a thermal capacity of about 100 kW h as a part of small solar plant based on the organic Rankine cycle (ORC). The phase change material (PCM) used is solar salt with the melting/solidification temperature of about 220 °C. Thermophysical properties of the PCM were measured, including its phase transition temperature, heat of fusion, specific heat, and thermal conductivity. The design of the thermal storage was finalized by means of the 3D computational fluid dynamics analysis. The thermal storage system is modular, and the thermal energy is delivered with the use of thermal oil, heated by Fresnel mirrors. The heat is transferred into and from the PCM in the casing using bidirectional heat pipes, filled with water. A set of metallic screens are installed in the box with the pitch of 8–10 mm to enhance the heat transfer from heat pipes to the PCM and vice-versa during the charging and discharging processes, which take about 4 h. This work presents a numerical study on the use of metallic fins without thermal bonding as a heat transfer enhancement method for the solar salt LHTESS. The results show that the absence of the thermal bonding between fins and heat pipes (there was a gap of 0.5 mm between them) did not result in a significant reduction of charging or discharging periods. As expected, aluminum fins provide better performance in comparison with steel ones due to the difference in the material conductivity. The main advantage observed for the case of using aluminum fins was the lower temperature gradient across the LHTESS.