BQ2982: BQ298218 Over heat protection with external PTC Thermistor

Part Number: BQ2982
Other Parts Discussed in Thread: TMP63

Tool/software:

I am trying to understand what thermistor I would need to connect to the CTR pin of the BQ298218 so that the battery is cut off at 60 C.

As I can understand from the datasheet, the voltage divider created between the internal pull up and the thermistor needs to produce a voltage greater than 1V to trigger the overheat protection. Assuming the worst case of a nearly depleted Li-ion cell at 3V supplying the VDD pin, the thermistor resistance would need to be 2.5M Ohm (given that the internal pull up is 5M Ohm).

The largest resistance PTC thermistor I have been able to find is the TI TMP63. At my target cutoff of 60 C, this has a resistance of only 125k Ohm. This means I would need to put this in series with a 2.125M Ohm resistor.

After the overheat is triggered, the battery remains disabled until the voltage of the divider reaches < 0.4V. Even with the thermistor resistance dropping to 0 Ohm, we still only reach 0.931V in the divider due to the 2.125M Ohm series resistor: the battery is now permanently disabled.

Now assume that we haven't permanently disabled our battery and it is actually outputting a more typical 3.7V. To produce a 1V in the divider we now need the external resistance to be at least 1.852M Ohm. Clearly this is always the case due to the 2.125M Ohm resistor we had to put in series so our charged battery will also become permanently disabled instantly.

It doesn't seem to be possible to actually select a PTC thermistor that has a resistance swing large enough to ever be of any use. This is really strange to me as the internal pull up could have just been a much smaller value, say 100k Ohm, and then the TMP63 would have worked ideally and the current would still be pretty low (50uA). There are 3 different pull up values available (1.5M Ohm and 8M Ohm in addition to the 5M Ohm) but they all seem to be completely useless?

Is there a different type of thermistor I don't know about, am I missing something else?