An innovative tree-shaped fin is proposed to address the problem of low thermal conductivity of phase change materials (PCMs) in latent heat energy storage units. Numerical methods are applied to investigate the thermal properties of the melting process of PCMs. This paper investigates the effects of fin arrangement, fin geometry parameters, and temperature of the heat source on melting characteristics of PCMs in the latent heat energy storage unit. Results show that the melting time of PCMs with the inwardly-tilted fins at the top increases by 21.3% compared to the outwardly-tilted fins at the bottom. The response surface methodology is adopted to obtain the fin parameter combination with lower quality and better performance. The optimal fin dimensions are a thickness of 1.06 mm, a length of 3.38 mm, and a spacing of 12.61 mm. The reduction of the ambient temperature from 35 °C to 30 °C increases the melting time of the latent heat energy storage unit by 85%, and from 35 °C to 40 °C decreases the melting time by 29%.