My roommates week old F56 with 452 miles has had an anomaly of sorts. Driving around tonight as you do in your shiny new cooper it suddenly started making an extremely loud whining noise in second gear. Almost a whistle sound like when you have the air vents almost closed. It's still there in third gear but more subtle. Any ideas?

 

No, but that doesn't have a good sound to it (no pun intended). They key is to get a dealer's service person to witness it and document it.

 

Could you be hearing the turbo whine? I'd get it to the dealer & have the level of the transmission fluid checked. Get this documented.