I decided to completely reinstall the operating system using the recovery tool. Observations:
1) The process went smoothly. I was able to use a recent backup to bring my phone back to where it was prior to the reinstall with no trouble.
2) The process caused virtually no heating issues, or battery drain. The entire process took around 25 minutes and the phone didn't get warm at all.
3) Reinstalling the apps, which is automated, took around 45 minutes. I didn't have the phone plugged in, and there was no significant heat, nor battery drain. The process used 2% of battery life (it was 98% when it finished).
4) I did the entire process with no memory card. After a few days, I will reinstall the card and report back. I am convinced that the memory card has something to do with this.
Other observation regarding memory card:
The memory card can be removed / installed while the phone is on. Installing the card causes SIGNIFICANT heat almost immediately, and it doesn't go away. I only have my new Samsung card to try this on. This is prior to re-installing the operating system; I haven't tried adding the card back yet.
The phone is now running cool, which it had been for a couple of weeks prior to it overheating again, as per when I first purchased my original 950, and started using my second 950 prompting the initial post.