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The thermal properties of epoxy‐based binary composites comprised of graphene and copper nanoparticles are reported. It is found that the “synergistic” filler effect, revealed as a strong enhancement of the thermal conductivity of composites with the size‐dissimilar fillers, has a well‐defined filler loading threshold. The thermal conductivity of composites with a moderate graphene concentration off_g= 15 wt% exhibits an abrupt increase as the loading of copper nanoparticles approachesf_Cu≈ 40 wt%, followed by saturation. The effect is attributed to intercalation of spherical copper nanoparticles between the large graphene flakes, resulting in formation of the highly thermally conductive percolation network. In contrast, in composites with a high graphene concentration,f_g= 40 wt%, the thermal conductivity increases linearly with addition of copper nanoparticles. A thermal conductivity of 13.5 ± 1.6 Wm⁻¹K⁻¹is achieved in composites with binary fillers off_g= 40 wt% andf_Cu= 35 wt%. It has also been demonstrated that the thermal percolation can occur prior to electrical percolation even in composites with electrically conductive fillers. The obtained results shed light on the interaction between graphene fillers and copper nanoparticles in the composites and demonstrate potential of such hybrid epoxy composites for practical applications in thermal interface materials and adhesives.