Hey Everyone,
I am experiencing a very similar issue with my 2014 Q50 Prem AWD. It has all of the packages(touring, tech, etc) as well. The issue I am experiencing has happened a couple times over the passed few years.
The most recent example of this issue happened to me this morning. I started my car this morning and drove to the store. The car started fine, it was idling around 1000 RPMs and drove totally normal to the store. I was in there for about 30 minutes, came back out to my car, went to start it, and it idled very hard and shut right off. I turned it on again and tried to give it a little gas to raise the RPM's. It stayed on, but a few different error lights came on(Chassis systems control malfunction, ML, power steering, change warning light, traction control). Also, the power steering would not work.
This has happened 2 other times over the past 2 years. Each of the other times that it has happened, I drove my car home, let it sit for a few hours, and then it would start back up and drive normal like it never happened.
I have also noticed that it always has a rough idle after I drive the car for a bit, turn it off to do something for 20-30mins, and then turn it back on. I am not sure why but I have seen a lot of other 2014 Q50 owners have the same issue.
The dealership nearby wants to charge me a $150 diagnostic fee just to look at the vehicle. I have a feeling it'll go away in a few hours but I was hoping someone else could shed some light on what the issue could be before the service department tries to tell me it could be 20 different things.