I agree about the People Mover - it was a favorite of my group of friends in the old days, and we used to love riding it because it was so long and relaxing and there was NEVER a line to get on it.
If you meant taking a break from rides and standing in lines and just the general hustle and bustle of the parks to cool off without a 'time limit' like would be the case with a ride (and believe me, I HATE hot weather so I will seek out any cool spot I can find), I would highly recommend the Animation Building. Even if you don't want to explore all there is to explore in there, you can literally just walk into the cool, dark main room and plunk down on one of the comfy chairs and watch the different snippets of Disney films on the screens above you. That is an excellent way to just sit like a lump for as long as you want and cool down. Something about the darkness of it is very calming, too. Yes, you could do the shows and Innoventions too, but those involve doing something more than just sitting like a lump. In the Animation Building, you literally don't have to do anything if you don't want to, except close your eyes and veg out!
I also particularly like sitting and cooling off in the lobby of the GCH (again - dim lighting = calming). We went in there last October to sit in the extra comfy chairs and chat and cool off a bit, and I swear I could barely move after 45 minutes or so. I was practically molded into the chair, I was so relaxed.