Boeing has recommended that carriers do not carry Lithium batteries in their holds. It will be upto the profit seeking carriers whether they comply with this recommendation.
I have a Galaxy S4 mini. It too gets hot, and sometimes for no discernable reason and drains the battery like a drunk in a bar getting free drinks.
Even when the Phone's Wifi/ GPS are turned off, and all apps closed, it will do so. Usually rebooting the phone stops this excessive mysto battery drain. Sometimes putting it in airplane mode stops the excessive battery drain, other times not.