When modeling thermal contacts with heat generation between two solids (e.g. electrothermal applications), we are often interested in evaluating the heat transfer rates and contact temperatures, and generally, it is difficult to evaluate these thermal characteristics due to interfacial conditions. In this work, a general representation of solid-solid thermal contact problems with heat generation is proposed. This representation is based on the thermal-electrical analogy and uses the notion of partition coefficient beta. The resulting equivalent thermal circuits are presented and discussed. The pertinence of this analytical approach is demonstrated for the electrothermal application of Joule heating for different contact configurations (similar and dissimilar materials, with and without interstitial fluid). The analytical results for each configuration are compared to numerical results obtained using numerical simulations under similar conditions, both results are in very good agreement. (C) 2019 Elsevier Ltd. All rights reserved.