We did ours on the ground last year and they worked fine. We didn't strap them down at all. We put black plastic down under them so we wouldn't have to worry about damaging the panels weedeating around them. We now have them on simple tables that are removed after the water heats up and we no longer need them until fall.

Interesting about the heat transfer CarlD mentioned. Sorta makes me want to put mine back on the ground.