I finally get my turn at dealing with a broody bird, and I can tell you that it has not been any fun. I am losing the battle with Doris Day, one of my Buff Orpingtons. She started going broody last week. At first I was worried that she was egg bound as she was lethargic and didn't want to move from the nest box. Then I went back to THE book, my chicken-raising bible, "A Guide to Raising Chickens" by Gail Damerow. This book has been my go-to resource in my now two-year adventure in raising chickens.
Doris has been showing all the signs of a broody bird: staying put in the nest, puffing up when someone comes near, pecking when we try to touch/move her, and not eating or drinking much. When a chicken goes broody, she also stops laying eggs. As the book suggests, I have been forcibly removing her from the nest and removing any eggs from under her that she has been attempting to incubate. But she keeps going back. I can't really try the trick with the ice cubes as all the chickens use the same nest (that's a whole different issue).
We may just have to move her to a different location until she finally lays an egg again. They say that for every day a chickens is broody, it takes the same amount of time to get back to laying eggs. At this point it will be another week to two weeks before Doris starts contributing.