In reply to james mann: Disclaimer: I am in no way an expert on rope safety!
I've had the exact same thing happen, but to a sterling rope a few years ago, again on the first use, at a wall and with several large but low factor falls.
Firstly, if whatever caused scorch marks was hot enough to scorch a rope then I suggest the durability of the rope can't really be called into question. If it was hot enough then it would have burnt any rope, they are after all made of the same stuff (well close enough that melting temps won't be vastly different).
Like you I ruled out the belay device as the melted rope was in the wrong places. It had to be the top QuickDraw where the heat had built up. This had never happened to me before, despite nothing in my climbing habits changing that night. I ended up concluding (rightly or wrongly) that it had occurred due to the rope being new, as a new rope holds it's shape far better it would be focussing more energy onto a smaller surface area and therefore building up heat quicker. At least once that night I had been lowered off reasonably fast after a lead fall (like you from quite a high clip) I'm guessing that the combination of all this plus the new rope being slick could cause sufficient heat to accumulate on the top draw. Like you I was very alarmed to find patches where the core was exposed and a melted sheath. I've since "bedded" my ropes in more on first sessions and haven't experienced the problem again.