My car did the exact same thing. Turned out to be the temperature sensor:
OEM / Performance Parts for Audi, BMW, Mercedes Benz, Mini, Porsche & Volkswagen - ECS Tuning
If your thermostat is more than 5 years old be sure to check that your engine is getting up to temperature as well. Use a scan tool to monitor it while you drive. Should get to 195F or so pretty quickly (3 or 4 miles), although in subfreezing weather mine struggles to maintain that with the heater running and non-highway driving.
OEM / Performance Parts for Audi, BMW, Mercedes Benz, Mini, Porsche & Volkswagen - ECS Tuning
If your thermostat is more than 5 years old be sure to check that your engine is getting up to temperature as well. Use a scan tool to monitor it while you drive. Should get to 195F or so pretty quickly (3 or 4 miles), although in subfreezing weather mine struggles to maintain that with the heater running and non-highway driving.