Your drum space is the same size as my Esmono drum booth. Enough room for a big kit.
If you've not heard of Esmono, they're two metal skins filled with rockwool panels.
My Esmono came equipped with an electric extraction fan, and long acoustically insulated air inlet and exhaust conduits.
I don't actually use the fans at all, as they're still noisy.
If I did use them, I might leave them on for practice, then turn them off while recording. Something you could think about.
Here in UK, my drum room doesn't get too hot.
I have a similar second Esmono booth in my dining room, which does get rather warm, with summer sunlight coming through a little window, plus all the kit turned on.
My solution for that is to open the door, and let the heat seep out, or not to use it too long during hot weather.