Just updated the ios version on my iPhone SE (ios 13.6) and the battery immediately began to drain by 1% every 7 seconds!! The phone heated up alarmingly during this time and after me rebooting it several times I’ve had to uninstall the app. Everything’s been fine since.
A simple Google shows that people are reporting battery drain issues and overheating in iOS 13.5 and 13.6 - some of them iPhone SE owners specifically.
A reason this can happen is that something in the update triggers the iPhone’s processor to keep working even when idle. It usually sorts itself out after a time or rebooting it a few times does the trick as you did.
When you perform an iOS update the phone performs a re-index of spotlight data, this is likely why your phone is overheating initially, it will likely be back to normal tomorrow morning.