Solid–liquid phase change materials (PCMs), promising for thermal management, face limited application due to leakage and low thermal conductivity. In this work, a shape-stabilized composite PCM was fabricated using a one-pot in situ process by mixing polyethylene glycol (PEG) with the novel metal–organic network called CFK, which was synthesized from carboxylated multi-walled carbon nanotubes (CMWCNTs), FeCl₃, and Kevlar nanofibers (KNFs). The morphology, composition, and thermophysical characteristics of the composite PCM were assessed. Key properties analyzed to validate its performance included leakage rate, thermal conductivity, latent heat, light absorption, photothermal conversion efficiency, and cycling stability. This composite PCM exhibits reduced leakage while maintaining remarkable thermal energy charge/discharge performance. The study establishes that the composite PCM containing 89.9 wt% PEG has a leakage rate of 0.76% since the PEG molecules are deeply embedded in the pores of CFK. The thermal conductivity of this composite PCM was enhanced by 170.5% relative to pure PEG, and the latent heat was measured as 147.9 J·g⁻¹ for fusion and 143.7 J·g⁻¹ for crystallization. Additionally, this composite PCM reveals excellent light absorption capacity, a photothermal conversion efficiency as high as 83.4%, and outstanding stability in photothermal cycling experiments. In short, this work offers a new strategy for both preparing high-performance composite PCMs and applying them in visible light conversion.