Most often if AC compressor/evaporator doing their job, and no joy on cold air, either the heater valve is stuck open or the hot/cold balance vane is struck hot. Usually in either of those cases, one side will work ok since left/right have their own hardware and controls.

The vent mix to dash is "both" however so that will throw you off. To determine if that is the issue send air only to feet and measure temp down there

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)