I have not had this happen with a GG as I dont own one yet, but I have had it happen with a stock 510. The first time I must admit was due to improper alignment on my part, I had it the oposite of the pics above.
I trimmed that cart about 1/8th of an inch, and aligned it correctly, then a week or so latter had the trimmed one totally melt down one side worse than the one in your pic.
At that point I just cut off the thin part upto the air intakes and use it just for a dripping mouthpiece. This works great, no need to worry about alignment when dripping, no need to worry about hot lips by tailpiping the atty either. I am currently using the cut down one on my protoge for driping.
I have noticed the whistle tips for 510 have thinner plastic on the part that would possibly melt, but I melted a thicker round one.
Now that I have my protoge in I notice it runs a LOT cooler than my stock 510 (same atty) This is because the adapter acts as a heat sink drawing the heat away from the atty while on stock 510 it just has the little battery that cant soak up nearly as much heat. As a GG also has more of a heat sink due to the adapter I would think it would act in a similar fashion and run cooler.
The AFS would also cool the atty a LOT I would expect!
(miniature nuclear cooling tank)