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This paper presents the dynamic model, analysis, and fuzzy control of a microchannel-heat-exchanger (MHE) space cooling network for dissipating exhaust heat of onboard electronic components inside spacecraft to the outer space environment. Along with a method for modeling a nonlinear fluid resistance network, a detailed analysis of flow rate changes and temperature transients of the MHE cooling network is given, providing a basis for developing a fuzzy coordination control strategy. The fuzzy controller employs two synergic PID controllers to simultaneously control both fluid- and radiation-based cooling mechanisms. The fuzzy coordination controller has been numerically evaluated, demonstrating a better performance than single-input PID controllers in terms of its ability to leverage between two actuators in rejecting disturbances and preventing overmanipulation. This unique feature will benefit the operating reliability of the MHE cooling network under stiff space working conditions.