As the dimensions of nanocircuits and nanoelectronics shrink, thermal energies are being generated in more confined spaces, making it extremely important and urgent to explore for efficient heat dissipation pathways. In this work, the phonon energy transport across graphene and hexagonal boron-nitride (h-BN) interface is studied using classic molecular dynamics simulations. Effects of temperature, interatomic bond strength, heat flux direction, and functionalization on interfacial thermal transport are investigated. It is found out that by hydrogenating graphene in the hybrid structure, the interfacial thermal resistance (R) between graphene and h-BN can be reduced by 76.3%, indicating an effective approach to manipulate the interfacial thermal transport. Improved in-plane/out-of-plane phonon couplings and broadened phonon channels are observed in the hydrogenated graphene system by analyzing its phonon power spectra. The reported R results monotonically decrease with temperature and interatomic bond strengths. No thermal rectification phenomenon is observed in this interfacial thermal transport. Results reported in this work give the fundamental knowledge on graphene and h-BN thermal transport and provide rational guidelines for next generation thermal interface material designs.