I think I might have an engine problem... :(

Was that video in fact with a cold engine?

Yes. It was running no more than a couple minutes and when I looked at the water temp gauge before shutting the car down, the needle never left 100F.

It usually takes about 5-10 minutes before the water temp reaches 130-150F. When it's running it never deviates from 180-200F, whether in traffic or on the track.