If the chickens like the shelf, let em have it! Is the shelf higher than the perch? If so, that's why they like it, chickens generally want to be on the highest perch possible. I have a shelf underneath my perch, and every day I scrape the poop from the shelf and put it into a plastic bucket. When the bucket is full, I spread it on my garden. Free fertilizer!
If your windows don't open, then removing one so it allows ventilation is probably a good idea. I would recommend you not cover it with chicken wire though. Chicken wire is not predator proof, and raccoons, dogs and other critters can rip through it. I would recommend 1/2" hardware wire instead. It is stronger and the smaller openings don't give as much opportunity for a predator to destroy it.
Living in Alabama, you probably don't have to worry about the cold. Chickens are completely fine in temps well below freezing. The only reason to close the window would be to keep rain out or if the window blows on the chickens as they sleep. A working window would be the best, so you can open it all the way when you want, and close it when you need to.
