i have something similar where during hot summer days w A/C blowing, it blows scalding hot air into the footwell.
I have not been able to solve it so far.
I know there are some regulator switches for each vent area, and it is computer controlled. Thought one of them needed replacing, but then one day i noticed the little side vents in the upper dash were also blowing hot air. The ones that point towards the side windows.
I had same issue with my old e39 and was never able to solve it.

Have tried diagnosing with Autologic, but nothing comes up.
I am living with it for now as it is colder outside, but at some point I need to leave the car with a genius who can figure this out.

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