Phase change materials (PCMs) offer a promising solution to the imbalance between energy supply and demand by storing latent heat. However, their low thermal conductivity limits their widespread application. To enhance heat storage efficiency, a triplex-tube heat storage unit was proposed with symmetrically arranged curved fins, and its performance was compared with that of a traditional straight-fin unit. The melting process within a triplex-tube system containing various curved fin arrangements was investigated. The results indicate that curved fins yield a stronger heat transfer effect in specific regions compared to straight fins. However, the inherent asymmetry of conventionally arranged curved fins reduces overall heat transfer efficiency. The symmetrically arranged curved fins demonstrate the potential to provide stronger convective heat transfer and a more uniform temperature distribution. Compared to straight-fin heat storage units, the melting speed of symmetrically arranged curved-fin units increases by 9.1% to 13.8%, and the average charging power increases by 10.3% to 14.1%. The fin configurations and enhancement methods offer a novel approach to fin optimization in thermal storage units.