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Suspended graphene has the highest measured thermal conductivity of any material at room temperature. However, when graphene is supported by a substrate or encased between two materials, basal-plane heat transfer is suppressed by phonon interactions at the interfaces. We have used frequency domain thermoreflectance to create thermal conductance maps of graphene contacts, obtaining simultaneous measurements of the basal-plane thermal conductivity and cross-plane thermal boundary conductance for 1–7 graphitic layers encased between titanium and silicon dioxide. We find that the basal-plane thermal conductivity is similar to that of graphene supported on silicon dioxide. Our results have implications for heat transfer in two-dimensional material systems, and are relevant for applications such as graphene transistors and other nanoelectronic devices.