With the rapid development of high-performance computing and artificial intelligence (AI), the energy consumption and cooling demands of global data centers continue to rise, and traditional ground-based cooling approaches face sustainability challenges such as high energy and water consumption. Leveraging near-continuous solar energy supply and deep-space natural cold sources, on-orbit data centers offer a novel solution for constructing green, efficient, and low-latency space-based computing infrastructure. However, in the vacuum environment, convective heat transfer disappears entirely, making thermal radiation the only effective mechanism for external heat dissipation. This imposes strict constraints on radiator area and mass. Simultaneously, the orbital day-night thermal cycling, phase-change heat transfer instability under microgravity conditions, and material degradation caused by space irradiation also present severe challenges to the design of thermal control systems. This paper systematically reviews the current development status and evolutionary trends of thermal control technologies for on-orbit data centers, outlining the key technologies, application scenarios, and development trajectories from three dimensions: passive thermal control, active thermal control, and integrated intelligent thermal control. It also summarizes the major bottlenecks currently facing research in this field. Finally, it outlines key development directions such as lightweight, large-area deployable radiators, microgravity phase-change stabilization mechanisms, system-level multi-physics field collaborative optimization, AI-based predictive control, and commercial deployment. The continued breakthroughs in radiation thermal control technology will determine whether on-orbit data centers can transition from concept validation to megawatt-scale applications, thereby providing critical support for the construction of future space computing networks.