I second what
@papbot stated. It might be nothing more than the usual maintenance tasks that run when you install the updated iOS. Also though, just because it is not widely reported, you still installed a beta pre-release build. There could be bugs that are negatively affecting battery life.
What the phone quite warm to the touch, one thing to note, at least this site(I am sure there are others as well) will run the battery more than normal. It has something to do with the ads on the site. This will also cause heat buildup right around the camera. Try using an adblocker and see if that helps.
If all else fails, you can always roll back to 15.1 but if you backed up at 15.2, that can be a pain in itself.