Abstract: The internal stability of widely used time-discrete temperature control system in spacecraft thermal control design will affect the temperature control effect. In particular, the stability of high-precision temperature control systems directly affect the achievement of temperature control accuracy. With a typical high-precision active temperature control system of a spacecraft as the research object, a unified temperature control system model that integrated the thermophysical model and control algorithm was established in this paper. And combining the engineering practice in spacecraft thermal control field, the model was linearized by reasonable simplification. Then based on the above linearized model, the stability of discrete temperature control system was studied. The mathematical analysis and classical control theory methods were applied to theoretically solve the temperature control system according to proportional and PI algorithms. The necessary and sufficient conditions for keeping the stability of the system was obtained. Finally, the correctness of the above constraints was verified by simulation analysis.