Something is wrong. The only place you want to get hot is the coil. Some of the heat will be conducted from the coil through the atty and into the mod. It hsould be hottest, warmest really, near the atty and get cooler the further you get away. It is also a sign you are
vaping too hot or too much.
If some other part of the rig is getting hot there is a problem. The problem could be in the battery or the mod. You need another battery or mod to find out where the problem is. Does the problem move with the battery or stay with the mod?
Heat is not good for a battery. It damages it. A battery that has been heated will hold less of a charge and might have other problems. If the battery itself is causing it to heat up then there is an internal problem with the battery.
Since you have a mechanical mod you must use an ohm reader to check the resistance of your atty and use Ohm's law to figure out how many amps it is drawing and you need to know what you battery is capable of supplying.
Also, the peeling green plastic is a serious problem. The battery is a metal can full of chemicals with a positive top. The negative part is not just the bottom but the entire can. The green plastic is an insulator that keeps the battery side from touching the mod and firing without you pushing the button. You can use electrical tape to cover a small tear in the plastic, take all the plastic off and use shrink tubing, for electrical projects, to build a new one, or throw the battery out. A battery with a damaged wrap is dangerous.
If you have an ohm meter with leads, not just one that the atty screws in, you can check the resistance of the button. It should be very low, almost non existant.