Thermal energy storage (TES) and harvesting is an effective technique for optimum building thermal management. Phase-change materials (PCMs) are commonly used for TES applications but are troubled by their degraded thermal conductivity. Recent research progress in latent heat energy storage using PCMs and nano additives provides a viable solution for solar TES. A series of hybrid nano-enhanced phase change materials (HNePCMs) were prepared via two-step synthesis. Hybrid graphene–silver nanofillers were dispersed in commercial paraffin (melting point 25 °C) under different dispersion rates (0.1%, 0.3%, 0.5%). Different characterization techniques, e.g., FESEM, FT-IR, UV-VIS, TGA, XRD, DSC, and Tempos, were used in material characterization. A maximum enhancement of 6.7% in latent heat and 5% in heat storage efficiency was noted for nanocomposites with 0.3 wt% of additives. The nanocomposite with 0.3 Wt% showed great potential in shielding UV rays and showed a reduction of 6.5% in bandgap energy. Furthermore, the thermal conductivity of samples was boosted by a maximum of 90% (from 0.2 W/mK-0.39 W/mK) with 0.3 wt% dispersion of graphene–silver nanofillers. The thermophysical characterization results establish that the synthesized paraffin/graphene–silver hybrid nanocomposites are well suited for building thermal management.