No they don't. The climate control remembers the temp scale.You can change the temp readout using the buttons as Kris mentioned, but they always change back to the default.
To make the change, I push two buttons on the climate control. One of them is the front defrost, I think the other is the auto button. The change is instantaneous. However, the minute I turn the key back to O, then on again, the default (celsius in my case) comes up.No they don't. The climate control remembers the temp scale.
I had an E46 rental in Germany. I set the climate control from C to F, it never changed back throughout my trip.