Heat exchange in vacuum largely works with a different principle and is much, much less efficient. Without other molecules to transfer heat to, we're left with black body radiation. Lower efficiency means bigger radiators. It's basically trying to cool down by giving off infrared light.

Something that could be done with a small coolant loop through a river or a glorified AC on earth, requires large sail-like structures in space (sails because it maximizes the surface to throw out that thermal radiation).