This one makes sense if the parents are old enough to have used silver nitrate film. Really old film can, and will, just catch fire on on its own if it's even moderately hot and dry.
Cooling down batteries literally saps their charge. Because there's less energy in the battery. You can gently warm up batteries to give them some extra charge.
The internet says that's not true (edit: at least for alkaline batteries, but for LiPo batteries I think you're right). It sounds like condensation is the main issue, so theoretically you might get a slight improvement if you put them in the fridge inside a plastic bag along with some desiccant.