Advances in 3D phase change composites (PCCs) are progressively transforming thermal energy storage and management through enhanced thermal performance and photothermal conversion. However, the arena lacks versatile materials tailored for a diverse array of geometries. This study introduces an innovative, shape-adaptive paraffin wax (PW) based PCC with shape memory attributes which are activated by solar and thermal energies, termed CuRNFFM@PW. Inspired by heat exchanger fins, the flexible PCC is synthesized by reinforcing a carbon fiber mat (CFM) with dense, uniform copper nano-network fins, which exhibit a lattice-like structure on the carbon fibers. The CuRNFFM@PW exhibits a substantial upsurge in thermal conductivity, reaching 1.79 W m-1K-1—a 746 % increase over pure PW and a 504 % improvement compared to CMF@PW. Furthermore, the composite boasts near-perfect thermal shape recovery (nearly 100 %), a good thermal storage enthalpy of 171.1 J g-1, and robust photothermal efficiency. Collectively, these attributes herald the CuRNFFM@PW as a promising candidate in solar thermal energy storage and in the thermal regulation of uniquely shaped electronic devices.