Thermal conductivity enhancement in a multiphase fluid such as water-in-oil emulsion can substantially improve efficacies in a broad range of applications. However, nanoparticle additives that are often used to do so can catastrophically destabilize a delicate emulsion system, in our case, a high internal phase emulsion (HIPE), whereas large concentration of additives can adversely impact practical processing aspects. Therefore, means to enhance the thermal conductivity of emulsions with a minute concentration of additives (<1 wt %) is a major scientific challenge. We report the enhancement in thermal conductivity of HIPE, by consigning either lipophilic GO (fGO) in the oil phase or hydrophilic GO in the water phase in combination with a well-known emulsifier. The rheological properties of fGO-HIPE showed non-Newtonian viscoelastic behavior similar to that of the original emulsion but with lower elastic modulus and viscosity, indicating that GO incorporation has enhanced processability. The thermal conductivity enhancements can be predicted by thermal circuit models, and the HIPEs with fGO and GO demonstrated 21 and 13% enhancements over the parent emulsion with a minor 0.1 w/w addition, respectively. A possible role of ordered colloidal structures of GO and fGO underlining this prepercolation behavior is inferred from comprehensive imaging and thermal studies.