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In this paper, we develop a methodology to obtain medium-order electrical equivalent circuits (ECs) of the thermal behavior of electronic systems. The method combines several elements: 1) the use of detailed finite-element (FE) simulations of steady-state thermal behavior; 2) graph partitioning of FE meshes to decompose the geometry at intermediate levels of detail; and 3) physically guided estimation of the parameters of the EC. To obtain richer training datasets, we also develop a method to include fictitious heat sources inside the FE model. This approach yields modular medium-order models for extensive and complicated geometries, such as a power-electronic chip. Moreover, representing the thermal behavior with an EC enables coupled simulations of electrothermal behavior, which are important in power electronics. We test our algorithms on a multimaterial pole of a dc motor and electronic chip. Excellent agreement in modeling both steady-state and transient behaviors was obtained.