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Mathematical model and control strategy are essential for active thermal control of nano-satellites. This paper presents a 5-nodal thermal network for transient performance calculation of heat-pipe thermal system which governs the temperature environment inside the nano-satellites. Two predictive control algorithms including implicit generalized predictive self-tuning control (IGPSC) and dynamic matrix control (DMC) were presented and discussed for the close-loop control of nano-satellite's heat-pipe thermal system, their control effects were numerically investigated and compared under different thermal disturbances. The numerical investigation results suggest that both IGPSC and DMC methods are effective for the nano-satellite's active thermal control. However, the control effects under DMC are better than that under IGPSC for excellent temperature tracking ability, fast responses and small overshoots.