Bottom gets hot. Definitely need to use the long legs and put it on the ground, or have some heat resistant slab between the stove and table. Don't recommend using any stove on or in a car - fire risk.
EDIT: For some reason I thought you were talking about the large 2-burner camp chef stoves. You're actually talking about the small / portable coleman though. I've never seen that one get too hot for tables as long as legs are positioned correctly, but no camp stove should be directly over any sort of carpeting / polyester / plastic. It doesn't take much to melt / scorch those materials. You're not dumb, it's an honest mistake.