Mama bird will spread her wings out to help cover more babies up. As they grow too big to completely fit under her, part of the baby will still be under her. Plus, in a natural setting (even in many secure coops) more birds will be lost to various causes, meaning that by the time the babies are two or three weeks old it isn't likely that mama bird will have as many babies to cover up. IN nature, predators and other accidents will have generally taken some babies. Compensating for these losses is part of why birds hatch so many eggs.
As the birds grow too big to fit fully under mama bird they start to gradually adjust to outdoor temps. Plus, at least where I live, a bird hatching babies naturally is probably going to do so when it's pretty warm outside, even at night.