First thing that comes to mind is. Are you the original owner. If not, then I’d say someone replaced the bulb with one that is way to high wattage. As far as i know, no reports of lens melting with oem bulb.
Just a stray thought. Could you have a bad connection at the bulb socket ? When I was working as a maintenance.engineer we used to ocassionally take thermal scans of all the electrical panels. A bad connection can generate tremendous heat. It is worth a look. ...J.D.
Have you hung a jacket over the headlight while leaving it idling? I've heard about someone melting the headlight on a BMW doing this.
That's not good, I'd take it back to dealers and see if they'll do anything under warranty or good-will at least if warranty has expired.
Are those melts definitely on the inside? Just double checking. In either case, definitely take it to the dealer. I have seen headlight melts when something exterior remains in contact with it for a while, but never from the inside.
Hi resistant joint can cause excessive current draw in turn creates heat. Check connections not scorched/ burnt etc.
Not sure of the cause, but when you find out you'll likely have to replace the headlamp! I've been looking for a used headlamp on ebay for a while as I am after a bulb shield and Triumph don't sell them separately. What I've learnt is that a new headlamp without shell etc from Triumph is about £450! eBay buy-it-now prices are all over the place, but when they are auctioned with a properly low starting price, they tend to finish up around the £15-£20 mark so it's worth waiting for one to come up Good luck finding a replacement! (oh, and if you do, any chance of the bulb shield from your old one..?)