In the period of 16.1.1, I also suffered excessive heat ‘points’ (meaning, my phone was excessively hot in certain areas of the phone); my battery deteriorated by 2%, from 100% full charge to 98%. I updated to 16.1.2, where it now no longer over-heats nor do I have battery-drain (I hope this lasts this way); my iPhone 13 Pro Max runs for nearly 2 days, BUT, I still have to have SIRI off, completely, AND, all my APPs I have all ‘background’ updates ‘OFF’ (I say all this, for 15.0 I had all settings ‘active-ON’ and my phone lasted over 2 days, where I was on the phone and internet for over 9 hours). Before you update, make sure you remove all APPs, then allow 24hours, then using a private network and your phone connected to a charger update, leave the phone ‘on’ from 9pm to 8am (there are peak times of background activities, I say this only because when looking at the battery chart it showed background activities) then individually re-install your APPs. This was the procedure had to do, like the old days with computers.