Head start

Up Mount Maxwell the air is 650s K, which is 380 °C; and at 4.7 MPa pressure. I've got a tower of liquid sulphur. Say I fill a cavern with that, and then drain it out without allowing more air in.

If we were keeping the sulphur at the same temperature, perhaps because the rock was poorly insulated, then such sulphur as hadn't drained will start boiling. West & Menzies, "The Vapor Pressures of Sulphur between 100° and 550° with related Thermal Data", The Journal of Physical Chemistry 33.12 (1928), 1880-92 peg a saturation of 380 °C sulphur gas at 268.5 mm of mercury. So: 35.8 kPA. Not much less than 1 bar.

I don't want a roomful of broiling corrosive gas - I can get that outside. Luckily I can assuredly react (or is it "reage"?) this vapour with some metallic dust and that will get me the pure vacuum for my upper server-room. Which is almost the first room I want.

For other chambers, I want air, just cooler air. First, obviously, I insulate such from the outside - not just airproof them.

As any fluid depressurises, its temperature drops. If we assume a phantasy sulfurlike substance solid only near absolute zero then the ratio P1/T1 = P2/T2 flips to T1/P1 = T2/P2. So 650/4700 = x/35.8, and the chamber is 4.95 K. LOL!

Sulphur will solidify long before that. Sulphur from 1 bar to 100 bar will freeze around 395 K. Specifically: into the "monoclinic" form. (The solid side of sulfur's phase diagram is like water's: complex.) Monoclinic sulphur is 1.957 g/cm3. However liquid sulphur on Earth isn't much less at 1.8. The liquid pressure that I've got at 395 K will be 2.86 MPa, to boot - ending up at near the same pressure in the end. If I fill a Venerean chamber with liquid sulphur and drain it out too fast, I risk a chamber full of solid sulphur. But cooler!!

So I suggest this: drain the sulphur back out slowly, or maybe in stages, allowing some air back in per stage. As the temperature cools it cools the new air with it. How much air depends on which chamber, in the end, but since this is the start of the colony I'm biased to keep the cooler inside air at the same pressure as the hellish outside or even higher.

I expect bedrock to be warmer than the outside. To keep the main chambers cool (and the vacuum room airless) we run the compressors. Cooling the low-atmo remains a challenge, absent liquid coolants. Venus air-pressures might allow for a wind coolant, especially on Maxwell's ecliptic east where I expect katabasis. Maybe compressed air can be exposed to the outdoor (5-6 MPa) wind and allowed back inside to expand to whatever. 700 K Carbon dioxide at 1 bar, according here, is 49.3 mW/(m K) but more like low 50s in the 50s bar range. Twice as good as Earth ambient nitrogen; a tenth as good as water.