Others mentioned it, but the stoves just don't get that hot. I always cooked on my tailgate, that had a plastic piece to match the bedliner. I used mostly a coleman 2 burner, but also a svea 123r. Neither would melt the plastic. I put hot pots fresh off the burner on the ground or on my wood cutting board or on something else non burnable like a leather glove.
I am always more worried about food contamination of plastics (mice!) than I am about burning them. Gold bond makes a great flame reducer....
James