With water in the pot and water, or dinner, in the bottle there may well be enough heat transfer to keep the plastic from melting to the pot base. That said, if you raise the bottle in some fashion even a small amount from the pot base, you'll be guaranteed water will circulate and keep it safely cool. Even a few pebbles would do the trick. Variables include the stove's flame pattern, the pot's metal and the type of plastic. For example, with a straight upward flame type stove and a titanium pot, I'd want a layer of water between the bottle and the pot.
(As to the off-topic topic, I'd at a minimum mind the type of plastic bottle used and choose one intended to hold hot liquids.)