Yes, but you need energy to pump heat, and that has an efficiency maximum (thx ~~Obama~~ Carnot), and radiative cooling scales with the ~4th power of the temperature, so it has to be really hot, and so it requires a lot of energy to "cool down" the already relatively cool side and use that "heat" to heat up the other side that's a thousand degree hotter.

All in all, the cooling system would likely consume more energy than the compute parts.

yes. it is how sats currently handle this. its actually exponentially effective too P = E S A T^4

requires a lot of weight (cooling fluid). requires a lot of materials science (dont want to burn out radiator). requires a lot of moving parts (sun shutters if your orbit ever faces the sun - radiator is going to be both ways).

so that sounds all well and good (wow! 4th power efficiency!) but it's still insanely expensive and if your radiator solution fucks up in any way (in famously easy to service environment space) then your entire investment is toast

now i havent run the math on cost or what elon thinks the cost is, but my extremely favorable back of hand math suggests he's full of it

You can. This is how it is currently done, but it is not easy. It needs to have a large enough surface area to radiate the heat, and also be protected from the sun (as to not collect extra heat). For a data centre, think of an at least 1000m2 heat exchange panel (likely more to train a frontier model).

Good intuition, that is generally how radiators work in space.

You definitely _can_ the question is, can you do it by enough for a reasonable amount of money. There are a few techniques to this but at the end of the day you need to radiate away, the heat otherwise it will just keep growing. You cannot keep pumping energy into the satellite without distributing the same amount back out again.

>>This is just a question. I have no expertise at all with this.

On the similar lines, why can't one run a refrigerator in space?

yeah if you want a heat thruster