Your technical info on the Lithium battery is also incorrect. It is not the temperature of the tire that effects the battery but the electrical load that dissipates the pacification layer which is what causes the apparent low voltage. Although the ambient temperature does affect the speed at which the pacification layer dissipates.
Regardless of exactly HOW the temperature affects the voltage, it does affect the voltage, which is what I said and it does explain why the sensor can apparently work fine in warm temps and not in cold temps.
Lithium batteries are almost impossible to know their life or capacity based on voltage because they hold their voltage very steady and drop so quickly (in contract to, for example, lead acid or alkaline, both of which have a very predictable curve). So the only way to know life to estimate it, based on an actual log of watt-hours used vs. full-charged capacity.... and that is complicated (especially since with rechargeables, the total capacity goes down with each discharge, and such calculations are what is done on laptops and phones and such). It is more complicated than can be reasonably accomplished in something like a TPMS. Thus, they have only a tiny, tiny fraction of a volt to indicate if they might be nearing the end of life, and that fraction is far less than the temperature variant... at least right when they start to show signs of failure.
Now, could they have moved the warning just a little bit more down the voltage range to extend the non-annoying service life of the sensor batteries? Probably... but it would also give less warning time. I can't say they could do a better job because not only I am not an electronics engineer, but I don't know their exact goals or what tolerances they have to deal with in the system.
The result CAN be annoying, no doubt.