I would suspect the voltage is low when cold. The alternator brushes cannot make full contact at the beginning and after the brushes get warmed up then you get the full charging voltage.
Do a test. Enable the cluster to display the battery voltage and monitor it from the start to when everything is back to normal.

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4.8is 2004 imola red
4.8is 2005 Black on Black - DINAN/2 sold
4.4 2004 X5
2003 330xi
2008 328xi - sold
4.4 2000 X5 - sold