I had the same heating/battery issue for many months and finally found a way to resolve it. Tried all the normal routes: resetting SMC, restating the machine, waiting for the indexing to complete, etc. The truth is, nothing really worked for me and it was painful to work on this machine. I feel that it is kind of sick (having a fever) due to some software bugs.
I think the root issue is with intel/apple's algorithm for turbo boosting (or some background programs triggering it constantly). In normal use scenarios, there is really no reason to turbo boost. You can see the issues clearly with the application called Intel Power Gadget. There are regular turbo boosts (frequency spikes every minute or so) even when the laptop is idling. This is bad software engineering. Resetting the SMC could not fix this issue.
I installed an app called Turbo Boost Switcher and with its help the temperature went down from 70+ C straight back to 40- C and the system is running smooth and calm again. If we use external displays/high graphics apps, the GPU may kick in and that increases the temps, but at least that is known/expected. If I plan to do some high performance tasks, I can purposely and temporarily turn on the turbo boost feature while plugging in the charger, and expect some high fan work periods. That is okay, too.
In my opinion the Turbo Boost feature should be turned off 95% of the time, unless the user wishes to have it. Otherwise it is a really bad user experience. With the turbo boost turned off, I am a happy camper and enjoying my macbook pro 16 very much again. Hope this helps you!