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A comprehensive thermal design to optimize the cryogenic cooling temperature of HTS transformer is presented, aiming simultaneously at compactness and efficiency. As small size and low power consumption are conflicting in determining the operating temperature, we develop a general and systematic model to quantify the effects of the temperature on compactness and efficiency. The procedure includes modeling of the critical property of HTS and the winding size, a heat transfer analysis for cooling load estimate, and a thermodynamic evaluation for cryogenic refrigeration. We demonstrate that there exists an optimum for the operating temperature that minimizes the overall power consumption, while taking into account the size effect of HTS windings. The optimal temperature turns out to be slightly above 77 K for two specific systems considered here: liquid-cooled pancake and conduction-cooled solenoid. The operation at temperatures well below 77 K can be justified, if the amount of ac loss is substantially reduced or the saving in capital investment earned by the compactness is significant in comparison with the operational cost.