Unless your nesting box is Huge, then it's not a good idea.
Mama will take them off the nest once they hatch and take them to food/water - this is why you provide a chick feeder and waterer that she and the chicks can access outside.
If you are concerned about her and her chicks moving about...
Photos?!
How large is the nesting box?
I would not put food/water in the nesting box. Provide food/water for Mama and chicks where they will roam once she leaves the nest with them.
If it's really hot, then no, I would not block ventilation off. She's been sitting in the same place this...