I have a Rent-a-coop one. I just finished a 3rd batch of chicks under it. Honestly, it does feel hot if you touch it. If you move your hand away even a little, though, you don't feel so much heat. Chicks are meant to be under it, not touching it, so they're ok. (They're fuzz sometimes does look...
Unfair, as I have chicks and take lots of pictures of them. This is my son, Chichetta, and Olive. The next most recent picture was a dead roach at my school. It was huge.
Don't worry about heat. But some clear tarps or plastic panels, and enclose at least part of the run to give them a wind-free place. Cover the roof of the run, too. They'll be fine.
What's a bigger worry is keeping water from freezing during those outages. Have a plan for that, be it solar...
Are her legs turning darker? If so, I suspect an Easter Egger or olive egger. But she's a pretty common chick color, and there are a lot of white adults, too. You can tell better when she gets more of a comb and leg color.
That being said, she also looks like my Columbian Wyandotte. I don't...