Frozen grapes and other frozen fruit are better than ice cubes for quenching thirst. I used to keep metal spoons in the fridge to suck on, too. That's really diet friendly. Also, if they have no AC, tell them to put the ice in front of a fan, not in their mouths. They should be cooling from the outside in, not the other way around.
Keep a spray bottle of ice water to mist over faces, heads, hands, and feet. Put cold towels on the back of your neck. Take a shower or bath in cold water. There are plenty of places that have AC that you can get into for free - a couple hours in the library is better than chugging fluid non-stop. Find the schedule for the local court house and watch some hearings. (Both safer than a mall, since there's nothing to buy!) Afternoon movies are good too, but only if they stay away from the salty popcorn.
Heck, it's Michigan - go sit a lawn chair in the nearest lake, put up an umbrella for shade, and sit in the water up to your chin. There's a lake every 7 miles in most of this state, after all! (I'm in GR - it's been brutal the last few weeks, hasn't it?)