A new analytical model is developed for predicting thermal contact resistance (TCR) of non-conforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach by employing the “scale analysis methods” is taken. It is shown that the mean size of the microcontacts is proportional to the surface roughness and inversely proportional to the surface asperity slope. A general relationship for determining TCR is derived by superposition of the macro and the effective micro thermal resistances. The present model allows TCR to be predicted over the entire range of non-conforming rough contacts from conforming rough to smooth Hertzian contacts. It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable and that effective micro thermal resistance is not a function of surface curvature. A comparison of the present model with 604 experimental data points, collected by many researchers during the last forty years, shows good agreement for the entire range of TCR. The data covers a wide range of materials, mechanical and thermophysical properties, micro and macro contact geometries, and similar and dissimilar metal contacts.