How can I acclimatize a recovering chicken from indoors to outdoors?

[JuliaSunshine]

I have a chicken that seems to be recovering from an illness I couldn't identify a month ago (Nov 3rd).
Since she got better a bit I let her out with other chickens during the day and brought her in at night indoors where temp is 41F-44F consistently.
But the weather turned so cold 2 days ago so I kept her indoors all day as she sometimes closes one eye, which has been going on for more than 2 weeks. She doesn't particularly get worse or better. She eats, drinks, and pops fine.
Now the outside temp is again about 36F during the day.
Is it okay letting her out during the midday? The temp swing will be less than 10F.

 

[Eggcessive]

If she has only been inside a couple of days, she should be fine if she can get out of the wind, or stay inside the coop. If they are inside for longer, it might be best to keep them in a basement or garage, where it is cooler to get them acclimated. But she also needs to be with her flock so they don’t attack her when she comes back. I don’t like for mine to be separated for more that 5 days, since there can be some pecking.

 

[JuliaSunshine]

If she has only been inside a couple of days, she should be fine if she can get out of the wind, or stay inside the coop. If they are inside for longer, it might be best to keep them in a basement or garage, where it is cooler to get them acclimated. But she also needs to be with her flock so they don’t attack her when she comes back. I don’t like for mine to be separated for more that 5 days, since there can be some pecking.

Thank you for your advice.
The indoor storage room at 44F is as cool as it can get for her to acclimatized in. I hope going from that to 36F isn't too much of a temperature swing for her.
It's hard to know what is best for her. I was worried her being indoors without sunlight and enough space to walk around for days might not be good for her.
Also I don't want to make her a total stranger to her flock even though they already chase her away since she was separated for a few whole days.
Because a couple of chickens that are low at the pecking order chase her away so diligently, she often stayed far away from the flock when she was out during the day. It's so sad.
I especially don't like one specific chicken following around and harasses her. That chicken has been such a headache attacking my feet and now became a bully to the weakest.