FYI; that's not how it works, you and the rock you mentioned in a different comment cannot have the same temperature of -18C. This is due to differences in material, and geometry to a lesser extent.
Even if you were rock-shaped, the rates of energy absorption and radiation is what determines your remains' temperature, this ratio differs for different materials, and thus difference fiilnal temperatures.
Why keep pushing back on this point? The total available energy from the sun in LEO averages about 1.36KW/m^2, and more than this can be radiated away by current deployed technology.
Solar powered space data centers probably make no economic sense. But not because we can’t cool them. We wouldn’t be able to run them very hot because there isn’t enough power there to do so.
No, not just a bit. It varies by hundreds of degrees depending on the materials α/ε ratio.
Your mental model is off: materials that good absorbers but poor emitters will get very hot, and the flip-side stay cool, and are used to make the cooling elements in the ISS . The temperature of ball of black nickel at 1 AU will settle at balmy 239C - not -18C. Polished Aluminum -> roughly 145C.
My nickel guy is gonna be so disappointed.