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This article deals with the electrothermal characterization of multi-turn windings in the magnetic components of power electronics (PEs) converters (inductors and transformers). The ever higher frequencies and smaller PE components demand the fast and accurate power loss computation for an optimal design accounting for severe electrothermal constraints. Homogenization techniques prove indispensable. Works on both electromagnetic and thermal homogenization exist but mainly consider both physics independently. We aim at studying the interaction of the strongly coupled systems when applying homogenization techniques. As test case, we consider a 2-D EI-planar inductor with two different multi-turn copper windings.