Better make sure that there is plenty of air movement in the crawl space. I'm not sure of the vent sizes but there is a formula based on the crawl space size to determine that number of square inches of the vents.
If fresh air blows in and out you shouldn't have a problem. It's the trapping of damp hot air that makes it like a greenhouse.
I've seen wood floors move to a 12" center peak b/c of lack of ventilation!
6 mil plastic and 30 weight felt should be put down too.
If done properly you can lay down anything ...even moisture sensitive hardwood.