Thanks for the ideas.

My daughter took it for an uneventful drive last night.

Figured I'd look into it today...

First thing, battery measured at 11.96V (as before, this at the jump ports in the engine bay)

Key in, to ON, shows 59*F. So unless someone snuck in and replaced my temp sensor last night ...

Carefully turned off all the HVAC and computer monitor nonsense that really wants to be wanted.

Try to start - click click click, instrument panel and computer monitor flashing, turning on, off, etc.

Repeated a few times, same result.

Battery read 11.5V after those attempts.

Hooked up a battery charger, ran it on 10A for a couple of minutes. No help. Got impatient, so I pushed the switch to the 50A engine start and it started just fine. Makes sense, if the battery is marginal.

So now it is parked in my driveway, getting a long, patient 10A charge.

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My thoughts so far:
That -40*F was probably the computer getting jammed up just like crowz thought. I had wondered if -40*F might instantly provide the answer, being such a specific clue. Guess not.

11.7V might be a weak battery in this case. I often have no problems with voltages in that range on cars, but this is more of a computer with wheels.

The battery is almost 4 years old, with a Feb 2014 sticker on it.

This car takes lots of pretty short trips, so it is entirely possible that the battery will live a little longer with some periodic full charges. I'll test this out and see how it goes.

Hopefully the solution will either be to keep the battery charged better, or to just replace it, and nothing more than those.

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2001 X5 3.0i, 203k miles, AT, owned since 2014