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But emit it to what? Vacuum cannot absorb heat.
There are 3 kinds of thermal transfer- conduction, convection, and radiation.
Conduction and convection are largely useless in space, all the heat basically stays in the same system, at most you can move it around do different parts of the same satellite/spacecraft, whatever, but you can't really get rid of it.
Which leaves you with radiation, which is not a particularly efficient way of getting rid of heat but you gotta work with what you got.
I cant give too detailed of an explanation because frankly it's a bit over my head, but this is where the stuff about infrared light being heat comes in. That's not technically true, after all, heat is basically vibrating atoms, and infrared light is photons, same as visible light just at a different frequency. Basically that vibration heat energy gets turned into photons and then just shoots off into space, essentially making all matter glow a bit in the infrared spectrum, and hotter things glow more.
And if/when those photons hit something else, it gets turned back into heat vibrations. Space is vast and mostly empty of course, so those photons could just keep flying through the void for eternity (I'm sure physicists could chime in and say no they don't and they actually lose energy and become some other kind of particle or something else crazy that's way above my head, but don't worry about that unless you're trying to be a physicist with a few years of college under your belt)
Lights work in space, so thermal radiation works in space. This is also the same way heat from the sun reaches us here on earth, there's obviously not a whole lot of matter between us and the sun for conduction or convection to carry the heat to us, it's just glowing and a bunch of those photons eventually hit us and make our atoms get all wiggly.
If you look at pictures of the ISS, in addition to solar panels, they also have big panels that serve as radiators to get rid of excess heat. They have coolant pumping through them to move heat from the rest of the station to the panels, but from the panel they're getting rid of it by just radiating it out into space. They're basically just sitting there glowing out all of the extra heat.
It a good thing there is no atmosphere between us and the sun. Apparently the noise would be deafening.