if the cooling fan is switching on at full blast - and you have errors on the dash, you probably have a situation where the engine ECU is going offline.

In my experience it can be either the ECU itself or moisture or water in the fuse block in the door jamb which is intermittently cutting out power to the ECU when cold.

Ive seen both, but the above is not exhaustive. to identify the issue you will need to see if the ECU is actually providing reference voltage to various sensors.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)