A critical component in optimizing hypersonic vehicle design and performance is to accurately predict the thermal response of the vehicle. In order to efficiently simulate the aerothermal interactions, a fully coupled conjugate heat transfer solver was developed. The simulations were performed with US3D, an implicit finite-volume unstructured compressible flow solver, with a newly developed implicit finite-volume unstructured heat conduction solver. The grids for the fluid and solid are non-face-matched due to the different grid requirements for fluid and solid. Results are shown for a simple two-dimensional cylinder test case, in order to analyze the accuracy of the face-matched vs. non-face-matched grids. Two and three-dimensional simulations are presented for a rectangular hypersonic inlet-isolator geometry. As expected, results show the heating of the solid in the isolator region is lower at the shock-wave boundary layer interaction locations when compared to the surrounding area.