You need to gently pluck some hair from the doe, and make a little nest for them with it in the back of that box. Otherwise they will grow cold and die. I am not sure if she will care for them. But here is something you can try doing. After you've made the nest, put the box in the cage and place a little bit of feed behind the babies. Momma should jump right in. The babies should be able to nurse while she is munching on the feed. You will need to watch her so she doesn't start stomping around on them. Nursing should take about ten minutes. The babies will have nice round tummies when they are well fed.What yu will want to do is take the nest box out to her twice a day for them to feed. Once in the morning. Once at night. Agian, give her a little feed each time. Once she realizes those babies are there, her instincts will kick in, and she'll feed them. I would do this until they are ready to come out of the nest box. Which would be at 15 days of age.
IMHO fostering them won't do any good. chances are you will only end up losing them.
Sometimes rabbits will go over 32 days when they are pregnant.