When formatting the Mac and reinstalling the new OS X, after entering their Apple ID login and password, many people are seeing this error message:
This Item is Temporarily Unavailable. Try Again Later.
The solution is to restart the computer, and as it starts, hold down Cmd + Option + R (not Cmd+ R as you probably did before). This will brig up the Internet Recovery Mode, wait for it, and then it will install correctly.
In my case it was initially attempting to install El Capitan and after doing this it installed MacOS Sierra - even better as it is the most recent version, as of this date.
Please leave a comment below if this solved it for you too.