Moving a Hen from Warmth Inside People House to Cold in Chicken Coop?

A hen had blood squirting out of her vent on Saturday and appeared to have a vent prolapse. The egg she had laid earlier had no blood on it. I took her in the very warm house (75 degrees?) and treated her vent with a warm Epsom salt bath, Neosporin, and Preparation H. The prolapse immediately corrected, without any help from me. I was worried about the area that had bled, so I gave her no laying food, just greens and vitamin water. The first day in the house she laid no egg. I kept it very dark so she wouldn't be as likely to lay an egg. However, the second day, same procedure, she DID lay an egg. She did not have a second prolapse or bleeding. So I'm thinking it is time to move her back outside where she can get exercise and be with her buddies. But... it is to be super cold the next few nights-- down to 8 to 10 degrees F. Last night I turned the heat down to about 60 in the house. She seemed to acclimate fine. But how should I reintroduce her to the very cold of the coop outside? I am so worried about shocking her. It is to be only about 30 degrees F outside today (the high), becoming colder as the week progresses. Tonight is to be 16 F (the low), and then the next few nights it is to be only 8-10 degrees F. I'm nervous. Any thoughts? She has 4 buddies in the chicken coop. The chicken coop is not heated, and I'm afraid to do so, for fear of a fire...

Put her into the coop at the warmest time of the day. This way the temperature swings are minimized. She is already cold hardy being in the coop during the past time. Taking her into your home for a couple days does not make her "soft"
WISHING YOU BEST.