John,
What size batteries were in play? The typical 2200mAH 18650’s can do 4 amps continuous for about 8 minutes as you alluded to before rated voltage falls off in my experience. Chances are very good your batteries PCB are rated for more than the battery can provide typically around 5.5-8 Amps of a 4 cell 14.4v battery.
So more likely than not the PCB opened due to voltage drop verses thermal run away as these devises do not have this feature. This means the cells dipped to sub 2.4V before they invoked the PCB’s discharge voltage feature and shut down.
FWIW: The current draw of an atypical 12VDC RV furnace is about 4 Amps, newer stuff sub 3 Amps. So you were asking a lot of your batteries (early in my life I was an RV Tech, fixed this stuff all the time).
I can assure you your batteries are worse for the wear, HEAT is the enemy and greatly reduces cell life expectancy, not to mention capacity and there is the depth of discharge consideration too. At this juncture your batteries have experienced a worst case scenario for preserving cell performance.
I record battery performance at various intervals and track performance thereof, age and such. This allows me to identify anomalies and garner information over the packs life cycle. If these were my batteries a note of the damage would find a spot on the spread sheet.
Future endeavors of this type are well suited for NiCad, NiMH and or Lithium Poly batteries; or even Lithium Ion if you have larger capacity batteries with cells stacked in parallel.
Multiple batteries would allow you to wire them in parallel, to increase capacity which increases the available discharge current or ampacity too.
Thanks for sharing.
Michael