I too am in a colder climate. Birds not used to a heated area can be stressed by it so I don't remove mine. Hopefully removing the top offender works, and the rest behave themselves.
It's normal for chickens to try to drive out sick or injured members, so they are acting normal. It can help to keep her penned longer, and figure it will take more time. I would use some wire to make a separation pen, especially if your crate is more solid, so she can be seen more.
Sometimes...