Ok guys, this is a weird one, let me break this down into steps to help the problem solving:
Diagnosis:
The alternator in the car is not the original Denso. I checked the voltage when it was whining after startup when cold and it was normal voltage at idle. After the whine went away, it was still normal voltage, so no difference in voltage when whining or when quiet. When it was whining, I unplugged the connector on the alternator, and the whine went away. I tried this on 2 different occasions during cold startup.
Repair:
I replaced the alternator with a new Remy one.
New symptoms:
When I first started the car with the new Remy alternator it had a very similar whine, but I couldn't tell if it was identical or not. I checked the voltage at idle during the whine with the new alternator and the voltage was normal. The whine lasted approx 3 minutes and then suddenly went away, it was a very quick distinct moment of going from a noticeable whine to quiet. I checked the voltage again, normal. The big difference is this time, when it was whining, I unplugged the connector from the alternator and it made no difference - the car still whined.
I am going to see if the car whines again tomorrow morning when I start it - at this point I am stumped. What else could be causing this whine? And what would cause a whine for a few minutes and then suddenly stop?