Why is my iPhone 5 constantly rebooting?

My iphone 5 started not charging past 1% randomly then It died and wouldn't come back on after being on the charger for 7 hours just doing nothing but showing the dead battery logo. It then came on and acted normal charging fine the whole day until that late afternoon it started randomly rebooting. The next day the rebooting got intense and faster unless plugged into a wall charger. Now its unusable even on the wall charger because it reboots every 3 seconds! Sometimes it just acts okay for a while until its pluged out of the wall then it reboots in a few minutes. The battery that I am having the issue with now is from another iphone 5....that hasn't been used that much exposed to heat drops or anything so it was basically better than the old one I had that died at 80% and drained fast. I know it shouldn't be any components because I put my phone in recovery mode so i switched the logic board from the other iphone i got the battery from and I am still having the issue? I did expose the phone to heat when it wouldn't come on after 7 hours but not more than 3 times 20 seconds each. Maybe it is the battery? I dont know I just need more answers. Never been exposed to water damage but a couple falls as the front screen is cracked and dropped on back a little.