They'd be shutdown by a dry contact that may variously be coming from the VESDA (Very Early Smoke Detection Apparatus), or an internal smoke detector, or a duct mounted smoke detector. Not as simple as flipping an obvious switch on a front panel.

First, the guy probably wouldn't have keycard access to whatever room contained such a switch. Second, it's highly unlikely that the system would be able to cool the room fast enough to avoid hitting the temperature limit.

Incidentally, we actually had a fire in the office building I worked in long ago. The HVAC didn't shut down, and smoke started to come out of random vents throughout the building. It was chaos. And yet, plenty of workers wanted to finish and send that email they were working on, commit code and push it to the remote server, etc. What sticks with me most is the one guy, a very senior manager, running around yelling at people to get off their computers and get out of the building, because no job is ever worth your life.

Building fires are no joke. Get the F out.