Hi,
have the waterpump and timing belt been changed? What’s the mileage? VAG group are well known for the water pumps failing before the belts and pumps can fail in different ways.
failing that I’d recommend getting a live data test done on the injectors, both at idle and during drive and see if any are running lean or rich. Especially considering the cold temps of the diesel in your climate.
if one injector is overfueling or underfueling this is likely to cause the engine not to get to temperature.given it’s an older Audi I can assume it has some mileage on it.