I encounter a lot of Toshibas, particularly the C655D series that have if not one, both hinges torn from the bottom. They have two screws that usually come off with the nuts and because of the hinges moving, the posts holding the palmrest screws right next to the hinges are also busted. I usually fix by isolating with modeling clay and masking tape then filling the lower hinge up until the screws are covered with epoxy. I use loctite for plastic, readly available at Walmart.
I would be interested in how you would do this kind of repair.
I know, it would be better to just replace the bottom, but it takes me less working time to do this repair, and just wait one day for the epoxy to cure.
Thanks for the heating tip, that's one that I will definitely do.