You do have a point as since there are very little air in space there is practically no heat convection to carry away heat, the biggest form of cooling on Earth. But there is still radiant cooling. Anything will emit black body radiation depending on its temperature. So while the front of the spacecraft is baking in the heat from the Sun the rear of the spacecraft is slowly cooling off from this radiant cooling. For the International Space Station you can actually see the white radiators it use for this purpose from some of the angles. They are smaller then the solar panels and angled very differently. These circulate ammonia which is used in the cooling loops on the station.
Things like the Voyager Probe is far away from the sun and can radiate what little heat energy it has. (Gasses between stars are around -455 °F) The James Webb Space Telescope is closer to Earth (and the Sun) so it was built with a solar shield that looks like a shiny umbrella so that it can reflect most of the sun’s energy and keep the telescope in the shade. It also has a cryocooler to conduct heat away from the instruments and then radiate the heat into space. (Gasses at this distance are about 45 °F)
Side note: ‘the vacuum of space’ is referring to how little gas is present: about one hydrogen atom per cubic meter- not really related to vacuum cleaners which is a machine that is like a mechanical drinking straw
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