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This paper proposes a data-driven supervised machine learning (ML) for online thermal modeling of electrically excited synchronous motors (EESMs). EESMs are desired for EVs due to their high performance, efficiency, and durability at a relatively low cost. Therefore, obtaining precise EESM temperature estimations are significantly important, because online accurate temperature estimation can lead to EESM performance improvement and guaranteeing its safety and reliability. In this study, in addition to the default inputs' data, EESM losses data is leveraged to improve the performance of the proposed ML approach for thermal modeling. Exponentially weighted moving averages and standard deviations of the inputs are also incorporated in the learning process to consider the memory effect for modeling a dynamical thermal model. Using the experimental data of an EESM prototype, the performance of ordinary least squares (OLS) method is evaluated through a complete training, testing and cross-validation process. Finally, simulation results will provide the key performance metrics of OLS for EESM thermal modeling.