I use Teslafi,
TeslaFi.com Tesla Model S X 3 Data Logger, and have found it invaluable for the data that is available, such as Battery heater, as it has helped me confirm or determine things such as longer charging times due to being throttled to a max of 95 kW instead of 110-115 kW when it was new or when to move stalls as a charger is only providing 150A instead of 250A.
You have correctly guessed that both the battery pack AND the supercharger should be at optimal temps for charging times to be as fast as possible. I haven't tried this yet of waiting at a supercharger for 4 hrs and using a stall that hasn't been touched during the time vs using a stall that someone just used for an hour. I would guess that the total time difference would be less than 5-10 minutes and I rarely have that tight of a schedule on road trips so a few extra minutes isn't detrimental. Annoying sometimes, but not detrimental.
I'm not sure what the optimal temp range is for the supercharger but in temps over 90 F the charging is also limited -- either from the car or from the supercharger or both. Maybe try it again or a different one with about the same starting SOC and see if it gets above 45 kW. You should also be able to see the Battery heater icon on your mobile app on the Climate screen if you can catch it in the 5-10 minutes it might be running.
In cold weather, just estimate that the car will require 150% or the distance being driven. Driving 100 miles then charge to 150 miles. Warm weather this can be as low as 115% - 125% and offers plenty of buffer but running full heat and A/C defrost and max fan speed really uses up the range quickly so plan for that and there shouldn't be any anxiety.
If you are charging every 50-100 miles then just estimate 30 minutes per charger. If you end up only needing 20 minutes per charger 4 or 5 times then you save almost an hour on that day and IF there is a slow supercharger the you've already accounted for it or if 4 of the 8 are blocked by snow piles and you end up sharing a stall with someone. Those are my cold weather tips and tricks.
For example, at the Grasonville, MD charger, you can see how the kW dropped right away as the Battery heater was on and then the charging rate slowly increased once it turned off (at 13:02). Normally, my max Volts are ~380-90 so that was fine and my max Amps are ~245 so the Amps were severely down even after the Battery heater shut off. It might have been a slow charger to begin with but the Battery heater wasn't on at the North East or Aberdeen locations and I saw 90-95 kW numbers. 26 minutes to go from 26% to 50%? Ugh.
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