The wire cage will do the trick I just wouldn't hang her in a tree.As long as the bottom is wire and is elevated enough to get a breeze under her it will work.This time of year 3-4" will work in the summer I use 2 sawhorses and a fan to cool her down. Try the cage for 2-3 days and then let her out to see how she acts. If she's still broody back in the cage she goes for another couple of days. Just make sure she has food and water.
I think the consensus here is that the underside of the chicken needs to get cooled off a few degrees ..... the dunking method in the video would be a bad idea this time of year where I'm at ...... as would a wire cage for days (tonight the low is supposed to be in the single digits ..... that'd be REALLY bad for feet on metal wire ......
You could probably use a wooden bottom to break 'em in the winter if it's below freezing...just no bedding.
My experience went like this: After her setting for 3 days and nights in the nest, I put her in a wire dog crate with smaller wire on the bottom but no bedding, set up on a couple of 4x4's right in the coop and I would feed her some crumble a couple times a day.
I let her out a couple times a day and she would go out into the run, drop a huge turd, race around running, take a vigorous dust bath then head back to the nest... at which point I put her back in the crate. Each time her outings would lengthen a bit, eating, drinking and scratching more and on the 3rd afternoon she stayed out of the nest and went to roost that evening...event over, back to normal tho she didn't lay for another week or two.
Water bottle with nipples added after pic was taken.