Hi I_break_it
You are right, the phone should always be off and battery disconnected when working inside the device. Luckily, you will be able to disassemble the phone and disconnect the battery before anything else, so there isn’t anything to worry about.
The heat you use on the back glass won’t cause any damage if the device is on or off.
What you shouldn’t do is start pressing and holding the buttons without any feedback on the screen. There’s a good chance you will put the phone in recovery mode and possibly wipe the device by accident.
Best of luck with your repair!