That’s not the issue, though. In a vacuum there is no medium with which to carry the heat away. You can’t send it into the air with fans or heat sinks because there isn’t any air.

At least on the moon you could sink it into the ground. But in orbit you don’t have that luxury. This is a major problem that spacecraft and satellite designs need to work around, and much effort is expended in that department.

Even though space is generally considered “cold,” in the absence of a medium to sink heat into the best you can do is rely on infrared radiation which is not terribly effective.