> Why? It doesn't take exponential effort to cool a space. It's linear.
It’s not linear at all. Going from 300 K to 250 K is much easier than going from 100 K to 50 K. If it were linear, going all the way to 0 K would be trivial.
The reason why it does not matter much is that average temperatures are not that different (Arizona is 29°C; Iceland is 14°C); the difference is not going to matter when cooling something from 300 K to 80 K. Besides, atmospheric temperature does not matter too much for underground facilities, and there Iceland is more active (thus warmer) than Arizona.
That said, things like proximity of an ocean, something with a huge heat capacity and decent thermal conductivity that could be used to dump heat more efficiently than in the atmosphere would be a plus.