Orbital data centers promise near-continuous solar power and freedom from terrestrial grid, water, and permitting constraints — but their feasibility is decided less by silicon or launch cost than by heat. A GPU in vacuum has no exhaust fan and no cooling tower: its heat must first be acquired from the die and transported across the spacecraft without buoyancy-driven convection, then rejected to space entirely as thermal radiation, where the Stefan–Boltzmann law converts every rejected kilowatt into square meters of radiator and kilograms of launched mass. This bookshelf curates literature on that problem in three layers: the problem statement, where hyperscaler design studies (Google's Project Suncatcher, Starcloud) meet rigorous thermal and economic counter-analyses; heat acquisition and transport, spanning loop heat pipes, the ISS's ~70 kW pumped-ammonia system, flight-proven mechanically pumped two-phase loops, and the ISS flow-boiling experiments now supplying the microgravity two-phase database; and heat rejection, from NASA's canonical radiator surveys and liquid droplet radiator concepts to megawatt-class kg/kW trade studies and the ISS's decade of radiator flight scars.