Topological fins can significantly improve heat transfer in latent heat storage units. In this study, a two-dimensional topology optimization model for a shell-and-tube latent heat storage unit was developed and experimentally validated. The optimal fin for different operating conditions and charge-discharge cycles was investigated. Box-counting dimensions and fin surface areas per unit length were used to characterize the topological fins. The results showed that increasing the charging time simplified the fin structures, whereas discharging times of more than 600 s extended the fin tips. For the 3000 s charge-discharge cycle, the optimal fin increased the surface area per unit length by 80% and the discharge energy density by 37.6% compared to the fin for the 3000 s charging process. The topological fin for a 300 s discharge-charge cycle with an extended branch resulted in a 7.7% increase in heat storage density.