We performed scanning thermal microscopy measurements on single layers of chemical-vapor-deposited (CVD) graphene supported by different substrates, namely, SiO2, Al2O3, and PET using a double-scan technique to remove the contribution to the heat flux through the air and the cantilever. Then, by adopting a simple lumped-elements model, we developed a new method that allows determining, through a multistep numerical analysis, the equivalent thermal properties of thermally conductive coatings of nanometric thickness. In this specific case we found that our CVD graphene is "thermally equivalent", for heat injection perpendicular to the graphene planes, to a coating material of conductivity k eff = 2.5 ± 0.3 W/m K and thickness t eff = 3.5 ± 0.3 nm in perfect contact with the substrate. For the SiO2 substrate, we also measured stacks made of 2- and 4-CVD monolayers, and we found that the effective thermal conductivity increases with increasing number of layers and, with a technologically achievable number of layers, is expected to be comparable to that of 1 order of magnitude-thicker metallic thin films. This study provides a powerful method for characterizing the thermal properties of graphene in view of several thermal management applications.