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Towed from Needles SC... long day.

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Our first out-of-state cross country was off to a great start: Santa Fe to San Diego, returning via Joshua Tree Natl park. Hot, but oat not greater than 110F, a/c blowing cold. Needles SC: red ring, console has 4 error messages including 12 volt battery, car won't start, call service. Service queries car, confirms "problems." Sends tow from Kingman, reserves rental in Bullhead.... Wait an hour; car will now charge, will move under own power (tested a few feet), oat indicates 135F!, "diverting cooling system". Tow arrives, temps down, all appears good! I tell Service, they query car again, still want to tow to Phoenix. Good service model, no argument from me.... Any insights appreciated. Is this the traditional 12 volt battery problem? Known temperature sensitivity? A fluke? Any ideas about time to repair? 85D, 2.5 months old, 8K miles. Thanks. First gasoline fill-up on rental cost $28! I had forgotten....!
 
Lead Acid battery output Voltage has a negative temperature coefficient of -5mV/˚C/cell. The starting point is usually 25˚C or 77˚F. Assume the battery is at 45˚C or 113˚F; that is 20˚C higher than nominal.

20˚C*6cells*0.005mV/˚C/cell=0.6Volts

That means a nominal 13.2 Volts on a charged battery becomes 12.6 Volts. This could make a battery appear weak; OTOH, I hope that Tesla temperature compensated the batteries...
 
My 12 volt gave me the bad signals at the supercharger in Squamish BC, didn't start, then did start, "do not proceed" call the nearest SC, etc. i called tesla, seattle, they had Vancouver call me. I waited, they ran the car thru some diagnostics over the system, told me, if this is right, that it would take some unknown amount of time to run thru my data, as my car hadn,t "checked in" for a while. I sat. Finally, multiple calls back and forth we decided to make a run for it to Whistler.. Felt "lucky" .The plan, if it stops on the way north, call us, we,ll bring a loaner and tow the car back to Vancouver. If it stops on your way between vancouver and seattle on your way home, call me, service manager gave me his personal cell. "I will either bring you the loaner if closer, or seattle will bring you the loaner" and we,ll tow your car to the nearest service center. It was not hot. They said basically "do not turn your car off". We got north, and all the way home a few days later. Car plugged into 110v. Tesla seattle took it in the next day. 10:00-ish, i had my car returned to me before 4:00 with new 12volt. Same day. Seattle SC and Vancouver SC get ten gold stars in my book. Thanks very much. My car is older 2+ years, i had been expecting the 12 volt problem for a while. After reading here. Sorry yours was on so new a car.