The porous interconnected structure of three-dimensional graphene (3DC) combines the excellent thermal conductivity of graphene with an interconnected architecture, thereby creating a thermal network within composites infused with 3DC. In this study, improvements in thermal conductivity, latent heat of fusion (H-f), and shape stability of paraffin were compared between paraffin phase-change materials (PCMs) infused with 3DC and with discrete graphene flakes (GP) at the same filler loading to quantify the advantage of the interconnected structure. Paraffin infused with a 3DC of higher bulk density (3DC(H)) was also compared to identify the effects of increasing filler density. Thermal conductivity of the PCM composites was measured using the hot-disk method, and shape stabilization was compared through thermal cycling in an environment chamber. We found that the interconnected architecture of 3DC improved the properties of the paraffin matrix in multiple ways. 3DC improved the solidification process for paraffin with heterogeneous nucleation, helped retain the shape of the PCM composite over thermal cycling, reduced void formation within the PCM, and induced a large increase in thermal conductivity, which was 7.4 times and 5.2 times that of neat paraffin for composites infused with 3DC H and regular 3DC, respectively, with only a small trade-off in H-f.