I just turn the rifle upside down and rub an ice cube from the drink cooler up and down the barrel. Upside down (scope on the bottom) lets the water run down the barrel and not get under the stock. It melts the ice cube pretty fast but it definitely cools the barrel down quickly as well.

Been doing that in our 100+ degree summers for several years now and have never seen anything detrimental about it.

Your idea of keeping the ice in a plastic bag is probably even better.

Gunnery, gunnery, gunnery.
Hit the target, all else is twaddle!