When the battery is low they turn the cabin ventilation off (I might have been just lucky to defrost the windshield and the very corners of the front windows to see the mirrors once).
Besides that I had a Check Control message. I'm not too sure but I guess I saw the low battery error at the service after that... The state of the battery is controlled by the computer. If everything but the alarm is fine have the alarm checked. And keep the battery full.