We perform a numerical evaluation on the multi-physical field coupling effect to improve the interfacial thermal conductivity (ITC) of Gr/h-BN (Graphene/Hexagonal boron nitride) planar heterostructure. The model of Gr/h-BN planar heterostructure (C-BN bonded configuration) is built to investigate the effect of the multifactor coupling effect of different temperatures, N-doping concentration, and single vacancy concentration on the ITC. Finally, the Box-Behnken orthogonal model is established to determine the optimal value of ITC under the coupling effect of multi-physical fields by response surface analysis, and the optimal value of ITC is 14.456 GW m−2 K−1 when the temperature is 673 K, the single vacancy is 2.57 %, and the N-doping is 18.9 %. It implies that the proper coupling configuration is found effective in improving the interfacial thermal conductivity of the Gr/h-BN heterostructure. This work is hoped to help promote the thermal reliability design of graphene heterogeneous interface for related micro/nano semiconductor devices.