Ideas:
To help her stay warm at night, can you set up a
heat lamp near her in the coop?
For some short-term help, you can also
fill a sock with uncooked white rice and microwave it a couple minutes to heat it up. If she's in a nest or crate, you can put it close to her for her to snuggle against. It stays warm pretty long.
Try not to leave food out overnight for the chickens, so the rats won't have much to eat (They usually come mostly at night).
Also, if you are using food bowls or pans, the rats will poop and wet on the food, which can pass on disease or other problems to the chickens. Instead,
put the feed in rabbit-pellet-style feeders; then rodents may still eat food, but won't climb on top of the food and contaminate it.
Feeders also have a rim around the edge that keeps chickens from being able to scoop food on the floor. Food spilled on the floor, by default, becomes available to rodents overnight. It also becomes contaminated not only by rodents, but also by chicken poop and likely mold.
Chicken troubles can be so very hard on your heart, and hard to diagnose and solve sometimes. Very sorry you are having troubles with your dear one!