I recall lots of similar cold-weather demons when I lived in northern Alberta (no X5 at the time).

I would start with rechecking the coolant, using a different anti-freeze tester. Rule that out first. That should eliminate any chances of frozen hoses.

Don't worry about the windchill, your X5 doesn't have any exposed skin so windchill has zero effect. I do see that it is forecast for -31C/-23F on Friday, so that is plenty cold enough.

You could have a thermostat problem. Could also be a sensor fault. I would watch it closely in any case, as overheating can be expensive. Given the nature of the immediate gauge fluctuation, I would suspect an electrical fault.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue