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Your trailer is too shiny. :)
This appears to be the same phenomena that has melted plastic siding on houses. Sunlight reflected from nearby windows adds to the heat of direct sunlight, and the "combined" temperature exceeds the melting point of some plastics. Normally the house window is on a 90 degree adjacent wall.
(It seems one guy on here even melted his house siding with his nearby trailer, or trailer window, in the driveway if I'm not mistaken.)
EDIT:
I was wrong, the thread was the guys pick-up topper and truck mirror was melting.
Silverado dissolves itself: http://www.rv.net/forum/index.cfm/fuseaction/thread/tid/27369720 The thread might show up under a search for "melt or melted". I'm not sure, but some of this might be because of new E-glass characteristics. In your case, a brilliant white trailer might reflect enough additional energy to melt already sun-drenched carpet.
There was also a case in London(?) where a building was melting cars parked on a nearby street. I think the building was shaped concave, thereby magnifying the effect. Rather embarrassing for the architect.
Wes
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