Wrong battery,or not sitting in tray correctly battery contacted hood took a few days to rub through hood insulation.....seen that one before
This was actually the thought that first came to mine for me as well, remember the old Volkswagen Beetles with the battery under the rear seat? If Too Tall of a battery was put in and someone heavy enough sat on the rear seat the seat Springs would short out across the top of the battery and set the horsehair seat stuffing on fire.
The other thing I have seen happen is a hood prop with a broken clip actually work its way to the positive terminal of the battery and while it didn't burn the car up or start a major fire it did start a small fire and actually a burnt a hole in one of the ac lines
This was on a Honda Civic, that is something that you should look at as well I don't know where the hood prop is on a Camry of that era but it's a possibility.
On some cars the hood prop is in such close proximity to the battery there's rubber insulation installed on the hood prop from the factory. Of course over time this can fall off or be knocked off causing a similar issue that you had.
Did the positive terminal have a terminal cover on it?