I can tell you what the "problem" is with the school A/C.
2 weeks ago when I went in, it was hot in the part of the building the administrators have moved into (about 80 degrees) literally right below where my classroom is. So, someone with authority (a principal) has moved the thermostat much lower. The temporary office space has a glass atrium that makes it hot (the atrium is kinda pretty and many of the schools in our district have the exact same atrium as a common architectural design but it really messes with the heating and air conditioning). It is comfortable in the office now and really nice in my room (I like it cooler) since my room is most likely on their system and I have no atrium to cool and is on the north side of the building so no there is no sun to warm the room.
That being said, I certainly did not explain things in an HVAC manner. My dad fixed A/C for 40 years for Sears (he fixed mine 2 days ago - it had a bad capacitor). What I should have said was that the A/C can't really keep up with 2,500 bodies in it on a hot day but is really kicking butt now. On the flip side, the heat sucks except when the building is full of people.
Every school building I have ever taught in (5 in all) has had goofy heating and cooling issues. Hot rooms next to cold rooms. Rooms with humidity so bad that wood rots and metal rusts with Fungus growing on the walls or it is so dry that kids get bloody noses. I have taught with a coat on, used the overhead projector as a heat source, brought in so many fans that I can barely be heard over the noise - in the winter. It's always an adventure. In the summer, I may freeze or be soaked in sweat.