In the context of carbon peaking and carbon neutrality, there is an urgent need to develop an efficient and stable cold energy recovery scheme for LNG cold energy utilization in China. This paper reports the preparation of a thermally conductive melamine sponge synergistically enhanced with graphene and multi-walled carbon nanotubes (MWCNTs) (denoted as GAC-MF) via the physical impregnation method. N-dodecane ( DD ), thickened with fumed silica ( R972 ), was then loaded into the GAC-MF matrix via vacuum adsorption to form the shape-stabilized phase change material DD-GAC-MF. Viscosity evaluation showed that at the optimal R972 concentration of 6 wt%, the viscosity was 388.4 mPa·s while maintaining favorable flowability. Through repeated cooling storage-release cycles, the optimal density of the employed sponge was determined to be 19.2 mg·cm-3, and the optimal mass ratio of graphene oxide ( GO ) to MWCNTs was 4:1, resulting in a leakage rate of only 0.2530%. Scanning Electron Microscopy (SEM) images revealed the successful loading of graphene and MWCNTs in GAC-MF. Fourier transform infrared ( FTIR ) spectroscopy confirmed purely physical interactions between the components, indicating DD was effectively shape-stabilized and encapsulated within GAC-MF. Differential scanning calorimetry ( DSC ) measurements revealed that DD-GAC-MF had a phase transition temperature of -9.1 °C and a latent heat of 148.6 J/g. The excellent thermal conductivity of GAC-MF enhanced the cooling storage-release rates of DD while eliminating supercooling degree. Therefore, the DD-GAC-MF composite represents a promising low-temperature cold storage material.