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On those hot days, you can never get cold air blasting through the plane soon enough. So unfeathering it would get more air coming your way.
You dont have to unfeather the first one prior to starting the second one.
Our manual stated to keep them both in feather until the tow bar and/or external power is disconnected.
Must be a company specific thing for you guys, kinda like our rule of having to use flaps 15/yaw damper off in our 300's on certain short runways or intersection takeoffs.