Novel shape-stabilized phase change materials (SSPCMs) were synthesized based on polyamide 6-co-polyethylene glycol/graphene nanoplatelet (PA6-co-PEG/GNP) composites. The selective distribution of GNP within the PA6 phase significantly improved the thermal conductivity of the composites, even with a low GNP loading. This is achieved through the initial dispersion of GNPs in the molten caprolactam (CL), which has a significantly lower viscosity compared to CL-t-PEG, allowing for better GNP distribution. Upon rapid polymerization, the viscosity increases, locking the GNPs in the PA6 phase, thus facilitating the formation of continuous thermal conduction pathways. At 5 phr GNP, the thermal conductivity reaches 1.11 W center dot m-1 center dot K-1 at 25 degrees C, a 296.4 % enhancement over pure copolymer, achieving twice the conductivity of conventional PA6/GNP composites with the same GNP content. The composites also exhibit excellent shape stability and thermal reliability, remaining effective over 100 thermal cycles. Infrared thermal imaging and finite element simulations further demonstrate that, near the phase transition temperature, the PA6-co-PEG/GNP composites exhibit superior thermal performance compared to conventional PA6/GNP composites, with the thermal conductivity being enhanced due to the increased specific heat capacity near the phase transition point. This study highlights the potential of PA6-coPEG/GNP composites as high-performance materials for efficient thermal energy storage and management applications, offering a promising strategy for thermal conductivity enhancement with minimal GNP content.