Chosen Solution
Just replaced my battery in my iPhone 6s Plus and it worked for all about 15 minutes till it died rather rapidly. Also the hot was burning hot? What gives??
Unplug the battery and let it cool down. They putting the old battery back in and hope it works.
Go to your settings and click battery. Than press battery health. It might be a bad battery. If it’s under 85% I would get it replaced again. If that’s not the case, try reconnecting the battery a few times and leave it charging for a while.
Where did you get the battery from? If you got it from iFixit they you will be covered under warranty. To me this sounds like a bad battery. You’re phone is on the older side some some of those batteries could have been sitting around for awhile. Lithium Ion batteries can sit around for a decent amount of time however they are still loosing charge and this can cause major problems from them. I see this happen from time to time when we repair devices even with a product that comes from a reputable vendor. Get a replacement and you should be good to go.