Purpose -This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact. Design/methodology/approach -The rough surfaces, known to be physical fractal, are modelled using a deterministic Cantor structure. Such structure shows several levels of imperfections and including, therefore, several scales in the constriction of the flux lines. The proposed model will study the effect of the deformation (approach) of the two rough surfaces on the TCC as a function of the remotely applied load. Findings -An asymptotic power law, derived using approximate iterative relations, is used to express the area of contact and, consequently, the thermal conductance as a function of the applied load. The model is valid only when the approach of the two surface in contact is of the order of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results both in trend and the numerical values. Originality/value -The model obtained provides further insight into the effect that surface texture has on the heat conductance process. The proposed model could be used to conduct an analytical investigation of the thermal conductance of rough surfaces in contact. This model, although simple (composed of springs), nevertheless works well.