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A temperature estimation algorithm (thermal observer) that provides accurate estimates of the thermal states of an electric machine in real time is presented. The thermal observer is designed to be a Kalman filter that combines thermal state predictions from a lumped-parameter thermal model of the electric machine with temperature measurements from a single external temperature sensor. An analysis based on the error covariance matrix of the Kalman filter is presented to guide the selection of the best sensor location. The thermal observer performance is demonstrated using a 3.8 kW permanent-magnet machine. Comparison of the thermal observer estimates and the actual temperatures demonstrate that this approach can provide accurate knowledge of the machine's thermal states despite modeling uncertainty and unknown initial machine thermal states.