Abstract: The carbon nanofilms on diamond were obtained by irreversible graphitization of diamond at above 1000 0C. The exposure to plasma reduces the surface conductance of the carbon nanofilms on diamond as result of a partial removal of carbon and the plasma-stimulated amorphization. The experimentally observed exponential dependence of conductance G of the carbon nanofilms on temperature T can be well represented by a relation G = A exp (BT). This behavior is explained by a model based on the thermally vibrating energy barriers formed between the carbon nanoclusters constituting the thin carbon nanofilms. The empirical constants A and B relate to the density of the carbon nanoclusters and the energy barrier height between them respectively.