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Contemporary superconductor synchronous motors utilize high current density, high temperature superconductor (HTS) direct current windings that request special cooling technologies. This paper presents a preliminary study in the design phase on several aspects of the thermal stability of a small power prototype of an HTS motor. The model we developed is notional, aimed at investigating the design of the cooling system. We present electromagnetic field and heat transfer mathematical models, and their numerical implementation. The results outline the heat transfer mechanisms, the hot spot regions in the motor, and may provide information useful to the motor design.