Can you put ice on your phone?

Can you actually put ice on your phone? I've heard some people say it can help cool down a hot device, but isn't that just asking for trouble? Wouldn't the moisture from the melting ice damage the internals? And what about the risk of shock if the ice gets too cold? Is there any truth to this cooling hack, or is it just a dangerous rumor? I'd really like to know if it's safe to try this at home, or if I should just stick to fans and air conditioning to keep my phone cool.