Cats and summer heat

This is my first summer with Niko (or any cat, for that matter) and I have a few questions about how cats handle heat and humidity. We have AC units in our bedrooms, but not in the rest of the house. At first, I thought we'd be able to just leave our doors open a little bit so he could come and go as he pleases, but he hates being in a room where the door isn't wide open.. so he just doesn't even come in. Normally, it's hard to keep him /out/ of my room.

I've been able to lure him in periodically, but he doesn't stay for very long. Is it safe for him to be out in the house without AC for long periods of time? I frequently refresh his water and add ice to it in between changings, but is there more I can do to keep him cool? A dog owner friend of mine suggested wetting/dampening him down (yeah right), but that's just not gonna fly. Some cats might not mind that, but he'd flip out. Perhaps some ice packs with a towel on top?

Well, yesterday it was 95 degrees, if that's any indication. :/

Thank you all for your replies! I've been giving him fresh, cold water very often and luring him into one of the bedrooms to nap during the hottest parts of the day. Also, he's a short hair cat, and I "defuzzed" him with the FURminator to get any excess, loose hair off so it doesn't add to the warmth. Good news, though: the heat has forced him to get out of his "I'm gonna freak out if you shut the door" thing. I've been leaving my door closed, yet not clicked shut (if that makes any sense). He can, and often does, push the door open if he wants to come in- and keeping something behind it so it only opens wide enough for him to fit has been working on keeping the cool air in. When not in here, he seems mostly content to sprawl out on the tile floor underneath our dining table. Hopefully, this heat wave will subside soon.. but in general, the whole summer will probably be pretty close to this.

I actually had to take up all of his toys, though, 'cause he just wouldn't stop playing! He's such a nut, sometimes. In this heat, to be darting around the house after pink mice, is insane. And yanno what else is crazy? When he does join me in the coolness, he has to be all curled up against me. If I were in his place, I'd park my butt in front of the AC and sprawl out. I want /no one/ touching me. *giggles*

Heh, trust me.. it's been no picnic. And oy.. the humidty, which makes it soooo thick and disgusting, I can't even describe it. In the summer, I become a hermit and stay in my room when I'm home. In here, it's fine and dandy, but cooking in the kitchen feels as though I'm ten feet from the sun. As for keeping our doors open, that wouldn't work very well for a few reasons. We have a fairly large house, but tiny bedrooms and with the open floorplan, the cool air would just dissipate till you could barely feel it at all. And since we only planned on using these in the smaller rooms, we got small and low BTU units... it'd waste a lot of energy to try to cool the entire house with 'em.