A lot depends on your hardware. I've had server room temperatures hit 100+ degrees and not had any direct hardware failures. The machines in question were IBM Blade and Compaq ProLiant servers which have pretty robust system management features and will autoshutdown if heat becomes an issue however. I wouldn't be too happy if this happened to some of the "white box" and budget Dells I also manage.
I'm going to skip the tech part for now because what you have is really more of a management/budget problem.
Here's a question: how badly inconvenienced is the school when it doesn't have access to the server farm? If the answer is "not very" you're basically stuck. Cost to benefit is not there. And this is especially a problem if you frequently experience outages. By now,the staff has probably come up with work-arounds for getting stuff done when system is down.
Next question: would anybody (other than you
) lose their job or get disciplined by the state or the Feds if you lost everything that's on those servers? That would include elected officials responsible for budgeting and operations in your school district. If the answer is yes, you'll need to work up a risk assessment and spell out the cost of doing nothing. Hopefully somebody will be smart enough (or scared enough) to see wisdom.One thing I would definitely do is document your concerns in some formal way.
Write it up and give it to whoever you report to. Rule 1: Don't lose your job/client!
I had a brokerage client that had a failing MSExchange server. I warned them at least once a week that it needed to be wiped and reinstalled. They kept putting it off. Two years later it finally failed. They lost two years worth of contract and legal correspondence because Exchange backed up a corrupted database, which it then refused to restore because --- it was corrupted! Gotta love it.
The only thing that kept me from being sued by them (and possibly prosecuted by the SEC) was the letter I sent to their senior management where I spelled out the risks and consequences of doing nothing. In the end, we retained them as a client, and one VP lost his job. Scary stuff and best avoided.
From a tech perspective, does your server have management features? If so, you could have it monitor ambient temps and send e-mails via SMTP to notify you and someone at the school when the system is shutting down. You could also have your UPS notify the server of a "power restored" event and then also send e-mail so that somebody could turn the AC back on. Those capabilities are doable with what you should already have.
Hope this was helpful.