True about the calories, they do eat as much food as they need to satisfy calorie requirements. And since this hen has higher calorie needs for body condition and to keep warm, she needs a higher calorie ration. Protein is a less efficient source of calories, and produces ammonia waste...
Sorry but I disagree - as a supplement to a well-balance diet fat sources such as BOSS and scratch are nescessary to provide a very underweight bird with nescessary fat calories to allow her to keep herself warm. Protein will rebuild her muscles, but is a much less efficient form of energy...
She needs a balanced diet supplemented with extra fat. Feed her some scratch grain and/or BOSS a few times a day. Be careful to not oversupplement her, she needs to eat mostly a balanced ration that will replenish her vitamins, minerals and protein in a correct ratio.
Check her over carefully...