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.
Audio: Jehnert Flatline speakers, Mobridge M1000 DA2 prepro, Helix P-DSP, Zapco Z-150.6 amp, CIC iDrive upgrade
Performance: Cobb Pro Tune, AR Downpipes, ER FMIC/CP, DCI, RB turbos and inlets, KW V2 coilovers, Fuel-It Stage 2 pump w Ported fuel rail, Mfactory LSD