While solar thermal power plants are increasingly gaining attention and have demonstrated their applications, extending electricity generation after the sunset using phase change material (PCM) still remains a grand challenge. Most of the organic PCMs are known to possess high energy density per unit volume, but low thermal conductivity, that necessitates the use of thermal conductivity enhancers (TCEs) to augment heat transfer within PCM. In this paper, thermal performance and optimization of shell and tube heat exchanger-based latent heat thermal energy storage system (LHTES) using fins as TCE for medium temperature (<300 °C) organic Rankine cycle (ORC)-based solar thermal plant are presented. A commercial grade organic PCM, A164 with melting temperature of 168.7 °C is filled in the shell side and heat transfer fluid (HTF), Hytherm 600 flows through the tubes. A three-dimensional numerical model using enthalpy technique is developed to study the solidification of PCM, with and without fin. Further, the effect of geometrical parameters of fin, such as fin thickness, fin height, and number of fin on the thermal performance of LHTES, is studied. It is found that fin thickness and number of fin play significant role on the solidification process of PCM. Finally, the optimum design of the fin geometry is determined by maximizing the combined objective of HTF outlet temperature and solid fraction of PCM at the end of the discharging period. The latent heat thermal storage system with 24 fins, each of 1 mm thickness and 7 mm height, is found to be the optimum design for the given set of operating parameters.