Enhancing thermal energy transport is critical for the applications of 2-dimensional materials. Here, we explored the methods of enhancing the interfacial thermal energy transport across the graphene (GR)/hexagonal boron nitride (h-BN) heterostructure interface, and revealed the enhancement mechanisms of interfacial thermal energy transport by applying non-equilibrium molecular dynamics (NEMD) simulations. The computational results indicated that both doping and interface topography optimization could effectively improve the interfacial thermal conductance (ITC) of the GR/h-BN heterostructure. In particular, the enhancement of the zigzag interface topography led to a much better result than the other methods. Doping and interface topography optimization increased the overlap of the phonon density of states (PDOS). Temperature had a negligible effect on the ITC of the GR/h-BN heterostructure when the temperature exceeded 600 K.