Two-dimensional heterostructures offer a new route to manipulate phonons at the nanoscale. By performing non-equilibrium molecular dynamics simulations we address the thermal transport properties of structurally asymmetric graphene/hBN nanoribbon heterojunctions deposited on several substrates: graphite, Si(100), SiC(0001), and SiO2. Our results show a reduction of the interface thermal resistance in coplanar G/hBN heterojunctions upon substrate deposition which is mainly related to the increment on the power spectrum overlap. This effect is more pronounced for deposition on Si(100) and SiO2 substrates, independently of the planar stacking order of the materials. Moreover, it has been found that the thermal rectification factor increases as a function of the degree of structural asymmetry for hBN-G nanoribbons, reaching values up to ∼24%, while it displays a minimum (∈[0.7,2.4]) for G-hBN nanoribbons. More importantly, these properties can also be tuned by varying the substrate temperature, e.g., thermal rectification of symmetric hBN-G nanoribbon is enhanced from 8.8% to 79% by reducing the temperature of Si(100) substrate. Our investigation yields new insights into the physical mechanisms governing heat transport in G/hBN heterojunctions, and thus opens potential new routes to the design of phononic devices. © 2017 Elsevier Ltd