If you can get a cheap table fan to blow ABOVE their heads in the room, not directly on them, it will circulate the air inside. If you have a cool tiled shady spot inside it might even be cooler once cooled off than being outside with all its risks.
Put empty soda bottles filled with water in the freezer, then lay them inside the pen. They can lie next to it or lick off the condensation. Try to remove the labels if you can so they don’t chew on them.
Definitely check out BB’s info. on the subject. My favorite for a quick cool down is the turban. You moisten a washcloth with cold water, wring it out, then wrap it around their ears. The cool cloth touching the inside/outside of the ears cools them and makes their bodies cool down. If it feels good they won’t shake it off for several minutes at least. Same effect as when you apply one to the back of your own neck when hot.
I would say the damp towel on the side is fine inside as well. Might try a sheet which is thinner and cooler. Block out the sun with blinds and keep the room dark, too.