I have been using rubbermaid containers for years, as broody boxes. I even designed my coop to incorporate them as nesting boxes, so that I don't have to move any broody out of her chosen nest. I just move the container. I don't put holes in the top. Only in the upper sides. I put the box with a plywood piece about 3' x3' on top of the box for shade and insulation. Outside they go into a run. I have 8 (almost 4 week old) chicks with their Mama that have been outside since they were a day old. She keeps them warm.
I even did this once in the depths of winter. They were fine until one night for some unknown reason the Mama hen stayed outside her nesting box with 3-4 week old chicks and some developed frostbite on their feet. I have more space in the coop, now, so that won't happen again. I discourage winter brooding in my flock though anyway.
I wouldn't wait a week before moving them to the floor. She'll start taking them out in a couple of days.
I would put Mama and the brood into a separated area so she doesn't try to take them up the ramp. She will try to get back to the old box for a day or two.
Good luck,
Dale-Ann
