Aside from the normal considerations of exceeding battery amp limits and battery stress, how does the internal resistance of the battery come into play?
This is the part of a battery's specifications which I know the least about. However, a battery which has a higher internal resistance will be less tolerable to stress and overheating than a battery with lower internal resistance. High capacity
batteries (higher mAh) tend to have a high internal resistance, while high drain
batteries (IMR and IMR/hybrids) tend to have low internal resistance.
This is one of the major differences between ICR battery chemistry and IMR battery chemistry. ICR batteries require protection circuits built-in because without them they can vent flames and possibly explode. IMR batteries are inherently a safer chemistry, are more tolerant to heat and stress, and therefore do not require the same protection circuits.
Lithium ion batteries have what's called a PTC or Positive Temperature Coefficient circuit. This is built into the battery just above the positive terminal and is present regardless of any "protected" labels. The PTC is designed to raise the resistance of the battery as the temperature of the battery rises.
The theory behind PTC is that as the resistance goes up, the current draw from the battery goes down - Ohm's Law. This helps prevent most accidents from becoming catastrophic, but it should not be relied on. The PTC is designed to be unobtrusive and you can still over-draw the battery if you aren't paying attention. The PTC circuits can also fail if exposed to static electricity or from a faulty charger. When a PTC fails, it often fails in a position which allows you to continue using the battery without fault.
The tech engineers at Provape touched on the topic of internal resistance in the following thread:
Question for the tech engineers at Provape