Heat conduction requires a medium, but radiation works perfectly fine in a vacuum. Otherwise the Sun wouldn't be able to heat up the Earth. The problem for spacecraft is that you're limited by how much IR radiation is passively emitted from your heat sinks, you can't actively expel heat any faster.

There is some medium in low Earth orbit. Not all vacuums are created equal. However, LEO vacuum is still very, very sparse compared to the air and water we use for cooling systems.

The main way that heat dissipates from space stations and satellites is through thermal radiation: https://en.wikipedia.org/wiki/Thermal_radiation.

Hot objects emit infrared light no matter the conditions. The hotter the object, the more light it throws off. By radiating this light away, thermal energy is necessarily consumed and transformed into light. It's kind of wild actually