Purplecat,
You can go out and spritz the entire piece with water, then cover with the plastic again. Or if you tap on the back and it seems sort of hollow(dry) sounding you could soak a couple of lightweight towels or teeshirts and cover the leaf then cover with plasic. You can change the toweling/shirting as needed.I would hesitate to move the leaf until you are more sure that it won't 'flex' and break, that is so frustrating. Once you are sure of that if you want to soak it in a bath of water it would be beneficial. Or begin spraying it with a hose, while it is covered with the toweling.

Dena

If the towel is big enough to more than cover the leaf, let the ends sit in containers of water. I'm not sure about your heat there, but here the towel wicks water up and stays wet.

If the leaf is on a movable board, set it in the shade and let a fine sprinkler run over it, if you aren't under drought conditions.

Sue