iPhone 12 overheating

my iPhone 12 heats up a lot, I felt this gradually increasing and not from an update but apps like Instagram, YouTube hear my phone enough to make my hands sweat, I cant play any games, games like subway surfers heat it up to point that I can’t hold and higher demanding games won’t run for more than a minute before lagging or crashing. My phone being more than 3 years old still has 84% battery health but it has over 800 charge cycles and I usually charge up to 60 and drain it to 0 and played a lot of games during the lockdown. Up to 85 it deceased in just a year, but for the past two years it went down only 1. I think I should replace the battery it it is a bit too expensive for it to not work. I don’t care about battery capacity just the fact that I can’t play games on it. Should I replace the battery? Or is there any other fixes