iPhone 4s over heating and draining battery

I have the same issue, but my iphone 4s was water damaged.

The overheating motherboard is probably a hardware malfunction. In your case it's most definitely (in my case it is too, though you have physical damage as well)

I would suggest taking it to the shop, or if you fix stuff yourself you should remove back cover, and see if there is a physical damage to the outside of the motherboard where it was hit. If it is even slightly bent, surely you cracked something in there, a "fix it yourself" would be much too difficult for someone that doesn't know how to fix micro-electronics. Find someone who can fix it for a fair price.

If you do not see any physical damage to the motherboard, there still might be damage that your don't see. Looking under the hood will just make it clearer for you.

Fixing components on Iphone motherboards will require hardcore soldering.

Goodluck.