Hi, standard protocol for airports is to arrive 3 hours before takeoff time. I can tell you that even as an experienced traveler (been to Cuba many dozens of times) I still always try to be there 3 hours before takeoff time. The checked baggage usually stops 1 hour before takeoff. But still, 1 hour is never enough to do everything.
My best advice is to give it at least 2 hours. I would never take chances with a flight, because if you miss it, it’s a huge hassle.
PS, I’m pretty sure there is air conditioning at the terminal. It is not luxury at all, but the terminal is not bad and should be comfortable enough. What you can do is check your bags and get your ticket but then just hang around the airport a bit, without going through customs. There are some shops in the airport and the outside esplanade. And then, an hour before, you can pass customs (which is usually very fast). This way you don’t waste an hour in the terminal.
Take care!
