Ive never come accross this before, but would a little glue put it back together and fill the split up.
I have heard radiators and sun light are not good for the vinyl dolls, but there again I did take my reborn out on holiday with me, and she didn't suffer at all, thow I tryed to keep her out of the direct sunlight as much as possible.
Its a shame this has happened hope you fix her soon.