Start making the ride now, and keep it up through the heat of summer. Easy outbound, fast back home. You'll figure out just how much you're going to sweat on a hot ride in, and decide which of these methods work for you.
If none of them will be enough (some people will sweat a lot in a Texas summer), look at other alternatives.
Are your school custodians friendly? If they trust you not to abuse it, a $20 hand shower attachment turns a mop closet with utility faucet and floor sink into a shower stall.