Schools are often very challenging RF environments, my uni wifi was constantly overloaded as fuck, even the newly built engineering campus was
not great. And they ran a decent amount of APs, but there was also a fuckload of people there on wifi all the time, because lol engineering campus.
Assumptions about IoT availability in terms of bluetooth/BTLE or 2.4/5GHz might be challenging for sure. Especially inside whatever HVAC metal/concrete cage etc (just run ethernet). Still though I mean it's running on a legacy UHF (?) system right now.
There are some industrial ISM bands at like 900 MHz or 432 MHz or something, and you can get modem boards that run on that. The 432 MHz aren't too fast but you just need to send "thermostat X turn on" and get a confirmation back. Which probably should be signed commands so some some yahoo can't have fun with the thermostat, even on this system, hopefully. But still, in a lot of cases probably a commodity solution would work.