Measurements of the thermal conductivity of thin dielectric films in the last ten years have established that thin him thermal conductivity may be much lower than that of the corresponding bulk solid, by as much as two orders of magnitude, and that significant interfacial thermal resistance may be present along the film/substrate interface. We review such measurements of thin film thermal conductivity and interfacial thermal resistance, and use the heat conduction equation to determine their implications for the localized heating of thermally anisotropic thin films bonded to substrates. It is found that for surface heating an equivalent isotropic film can be established and that the presence of large interfacial thermal resistance leads to a strong dependence of film thermal conductivity on film thickness, especially for thin films. A microscopic model of the film/substrate interface is used to establish the dependence of the interfacial thermal resistance on porosity along the interface.