You can't just get rid of heat. To locally cool something, you have to heat up something else by more than the amount you cool the cold thing such that in the net you are actually heating the universe more.

Of course - which is why I mentioned expelling a coolant/reaction mass. Today's computers use a number of elements from the periodic table, but the distribution is very different than the distribution of matter in our solar system. It would be very unusual indeed if the element distributions over optimal computronium exactly matched that of typical solar system.

So when constructing an advanced low-temp arcilect, you could transfer heat to whatever mass is the least useful for computation and then expel it.

Limiting heat flow in and out of a cold object is quite possible. But if its DOING anything it will generate heat.

In theory with advanced reversible computing, there doesn't seem to be any hard limit on energy efficiency. A big arcilect built on reversible computing could generate extremely low heat even when computing near the maximal possible speed - only that required for occasional permanent bit erasures and error corrections.