Got my air yesterday and it definitely gets hot. Will see how it does after a few days as I expected the heat due to the initial sync and transfer, and iOS indexes everything for a day or two.

I have one, too, and you're right that the heating is just what happens while it restores its data and settings and whatnot.

I believe it also re-scans your entire photo library to re-identify dogs, cars, people, etc. with whatever improved algorithm comes with the new chip/OS.

This happens every time you get a new iPhone. Depending on how much it has to sort through, it can take a couple of hours to a week.

I always leave the case off for the first few days.

As a photographer with over 50,000 photos in my iCloud, getting new iPhones is a pain.