You did the right thing to move her to a new nest box, but that box should be in an area where she cannot go back to the old nest. If both the broody and non-broody hens are in the same coop, you'll need some type of barricade to give the broody her own area where she has to stay and other hens cannot get in. A broody pen can be made with any number of materials (e.g., a cardboard or chicken wire partition that is stapled to the coop walls). A 3x3' area should be sufficient, with the nest box (at least 14x14") occupying this area. One risk is that she may stop being broody when you move her, but it's also risky to leave her where she is and have other hens trample the nest.
You can also set up an entirely separate broody area for her with materials you may have on hand. I currently have a broody hen in a large dog house (approx 2.5' x 3') that is located within a 6 x 10' chain-link dog kennel. The sides and top of the dog kennel are covered with chicken wire to minimize the risk of predators trying to enter, and a portion of the top is covered with a tented plastic tarp for shade and rain protection.
If you think the eggs were cold for several hours, I'd recommend starting over with a new batch unless you can candle them and confirm they are still alive.
