Deep litter will retain warmth.
I personally don't bring food and water close to broody birds. The need to get off the eggs to defecate.
Wife was nice one time and fed/watered her on the nest. She let loose a huge broody poo right next to the clutch.
Nothing smells as bad as broody poo.
She will hatch them and raise them given the chance.
I've had a goofy broody this time of year. I usually keep 3"-4" mashed down straw in the nest boxes. When she went to ground after hatching I waited for her to settle in her spot, then gave a flake of hay for her to wallow a hole in.
Temps...