@soapeater this"heat even when turned off" would mean that there is a short somewhere on the board that cause the battery to create this heat. Disconnect the battery and check the battery connector as well as the components around it. I would expect this to be an issue with a power management IC. It's not the age, it's what may have gone wrong. WE really would have to see more of your board etc. to guide you further. For that, you have to take it apart. Select your model form here iPad Mini 4th Generation Repair and look through the guides and see if that is something you want to tackle. If not, I would suggest you get in contact with somebody who does board level repair. Since we do not know where in the World you are, we should not make any suggestions.