To address the application bottlenecks of organic phase change materials characterized by low thermal conductivity and susceptibility to liquid leakage, this study utilized natural poplar wood as a raw material to construct a three-dimensional carbon/silver heterogeneous porous skeleton via delignification, gradient carbonization, and in situ electroless silver plating. Polyethylene glycol (PEG) was then vacuum-encapsulated within this structure to prepare form-stable composite phase change materials (CPCMs). The regulatory effects of carbonization temperature and metal interface modification on the microscopic morphology and thermophysical properties of the materials were systematically investigated. The results indicate that the skeleton carbonized at 800 °C achieves an optimal balance between pore distribution and skeleton rigidity, ensuring the uniform conformal growth of silver nanoparticles and endowing the material with excellent anti-leakage performance. The thermal conductivity of the optimal sample reaches as high as 0.683 W/(m·K), with the melting latent heat maintained at 133.9 J/g, while also demonstrating an agile and stable photothermal conversion response. Non-equilibrium molecular dynamics (NEMD) simulations further confirm that the silver nanoparticle modification layer smooths the phonon vibration frequency mismatch between the carbon substrate and organic segments, significantly reducing the interfacial thermal resistance. This research provides an important reference for the structural design and microscopic heat transfer mechanism analysis of high-performance phase change energy storage materials.