First of all congratulations on your new i8 Coupe! Amazing car and there will never be another like it.
BMW does not have a "powertrain" warranty per se, if you don't have an ESC or CPO after the 4/50k. There are certain parts that may carry extended warr. on but that is on a VIN by VIN basis... That being said, however, some emissions components are covered if they fall under CA federal emissions guidelines. Your local dealer would have to diagnose the vehicle and you would be responsible for a diagnosis fee if you choose not to do the work, if it is covered it gets waived, or if you pay for a repair it goes away. That is my experience with BMW dealers. If something is under emissions warr. they will still have you auth. diagnosis. It kind of sounds more related to HVAC system but would be worth it to get it checked as I could very well be wrong since the e-drive is tied into so many things. And I would assume since the i8 is a plug-in, that it would get additional coverage like most PHEV's if they do find a failed part that is covered.
Good luck and let us know!