If all the energy for a space appliance comes from the sun, in steady state they only have to radiate away the same amount that hits them. All long-lived spacecraft manage it.
Whether they can be worth the money it cost to put them in orbit is another story.
> All long-lived spacecraft manage it.
Apples to oranges, long-lived satellites have modest power needs. Doing a back-of-the napkin math on required size of solar array and radiative elements for a single-rack's worth of energy is a sobering exercise for those who are a overly exuberant on the topic. The all-in power estimate for a single GB300 chip is 2.1kW
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