Right, but even there you still have the square-cubed law working for you - the larger volume you deal with, the less surface area you lose heat through.
Yeah you need to work very hard to lose heat without losing mass in space. Basically you can only radiate it away, which is slow; there are ways of concentrating heat in one spot so it is radiated more efficiently, but that’s where you get to the melting part.
Heat dissipation is actually a gigantic problem in space: you can only radiate heat away (and try to reflectively shield against the sun) since you're in hard vacuum which is a fantastic insulator.
What material would this have to be made of to not melt?
Edit: I'm not that familiar with radiation and its parameters/properties. My assumption was that it would accumulate heat. I'll go look up if radiation is a function of heat, then I suppose it could become stable at some temperature. It's surprising to me that you can block out some of the sun from a good area on the earth and not have melting bits.
What the commenter is pointing out is that it may not matter how you cool the reactor. It could be in interstellar space and it might not matter because the material the reactor itself is made of may not be able to transmit the heat away from the reactor. And no such material may exist.
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