Using thermal storage materials with excellent thermal properties in the energy utilization system enables efficient use of renewable energy sources. Organic phase change materials (PCMs) have the advantages of high heat storage density, no corrosion, and low cost, but low thermal conductivity and insufficient heat transfer capacity have always been the bottlenecks in their application. In this paper, melamine foam@ reduction graphene oxide (MF@rGO) and carbon foam@ reduction graphene oxide (CF@rGO) composite foams with double carbon networks were prepared by self-assembly method and further employed in 1-octadecinal (OD) PCMs. The microstructure, chemical composition, phase change behavior, thermal conductivity, and photothermal conversion performance of MF@rGO/OD and CF@rGO/OD were studied in detail using SEM, FTIR, Raman DSC, and LFA. The melting and solidification enthalpies of CF@rGO/OD composite PCMs were 208.3 J/g and 191.4 J/g, respectively, its thermal conductivity increased to 1.54 W/m·K, which is 6.42 times that of pure OD. The porous structure and high thermal conductivity of the double carbon network substantially enhance the efficiency of energy storage and release in composite PCMs. CF@rGO/OD composite PCMs have excellent heat storage performance and heat transfer capacity, and a wide range of application prospects in the fields of low-temperature solar heat storage, precision instrument temperature control, and intelligent buildings.