BMW cold start stalling / bad coolant temperature sensor

Car misfires and stalls during cold start.
No errors. (tested with BimmerLink and ISTA)
BMW F30 316i N13 engine (but the failure is quite generic).
The problem proved to be the coolant temperature sensor that was indicating the engine already warm.
The problem manifested itself with a rough start at first, as the cold season started.
After a while I got an engine stall on first start attempt, but it started fine on 2nd try.
After a few more days this problem (engine starting only on 2nd attempt) would happen every time the car was parked for a full day.
I got the car to a service center as I was not in a mood to investigate myself. They tried a few preliminary things but it was hard to diagnose without an error in the system. We agreed I'll get back to them when we get an error.
The car actually got worse when I took the car back from the service center but still no error. Now the engine would not run unless I help it by revving it for a couple of minutes until it could hold idle by itself.
So I decided to spend some time and investigate the problem myself.
What I first noticed was that the coolant temperature was over 25 degrees Celsius in the morning (car sitting over night) while the ambient temperature was zero degrees Celsius. I had some data logs saved weeks before and they were showing over 20 degrees coolant temperature in the same conditions. It looked like a trend - coolant temperature sensor showing higher and higher temperatures in the mornings. A similar log saved the winter before looked ok.
I decided to change the temperature sensor (3 years old Hella sensor) with a new one (original). This fixed the problem, indeed.

Видео BMW cold start stalling / bad coolant temperature sensor канала Cosmin Rotaru