Earlier quoted context omitted.
Considering the difficulty of dumping heat in a vacuum and the cost of orbiting huge heat exchangers, I wager that heavy computing shall remain a mostly planetary activity for quite a while longer.
Isn't rather chilly space a great cooler for anything that heats up?
Vacuums (or near vacuums) are actually good insulators. Double-walled insulated travel mugs are a great example of this.
Also, if you think about this in the context of the Sun, you get a really visceral feel for just how much energy is being produced. Black-body alone is transferring that energy to us. Scary.