Latent heat thermal storage systems (LHTS) utilize their latent heat capacity to dissipate high heat fluxes while maintaining quasi-isothermal conditions. Phase change materials (PCMs) absorb a large amount of energy during their phase transformation from solid to liquid, maintaining quasi-isothermal conditions. However, they are often beset with low thermal conductivities which necessitate the use of a thermal conductivity enhancer (TCE) as it is impossible to design a device that can completely avoid sensible heat in the premelting or postmelting phase. In this study, the heat transfer performance of LHTS with cross plate fins as a TCE is numerically investigated for different values of fin thicknesses and fin numbers along the length and breadth. A hybrid artificial neural network coupled genetic algorithm (ANN–GA) is then used to obtain the optimized dimensions for the composite heat sink with cross plate fins as TCE for a fixed volume and a specific heat flux input. The numerically optimized configuration is finally validated with in-house experiments.