The aim of this work is to comprehensively study the effect of the material of the simple plate and tree-shaped optimized fins on the thermal behavior of an enclosed medium filled with a nanocomposite of neopentyl glycol/ CuO solid-solid PCM. Increasing the heat transfer rate using a fixed amount of material is an important task that improves the fin performance. The tree-shaped fin is optimized based upon the density-based structure optimization method. A transient model based upon the enthalpy method is employed to numerically study the thermal behavior of the enclosed medium containing the SS-PCM. The thermal performance of the heat sink with the tree-shaped optimized and simple plate fins made of different materials are explored. Results show that the aluminum and copper fins have the highest melting rate compared to the examined materials. Their melting rate is 50% higher than steel 302 in the case of flat plates, and 25% in the case of a tree structure. Also, the tree- shaped optimized fins outperform the plate structure fins by reaching the lowest temperature of the concentrated heat source and temperature non-uniformity under the condition that the two strucutures have the same height. When the two heights are different, the temperature distribution was optimized for materials with the lowest thermal conductivity. For steel materials, a 10% decrease in the maximum temperature was observed in the tree structure compared to the flat plates. Finally, it was shown that the nanoparticle fraction played a negligible role in heat transfer, as less than 1% change in melting rate and temperature parameters was obtained.