Pregnant rabbits and babies in extreme heat?

I have 2 pregnant rabbits outside in different hutches due to give birth within the week. I already put in a nest box for each with hay and they have taken an interest in building a nest. I'm concerned though because we live in Houston, Texas, and it's the hight of summer. The temperature has been getting into the 100's the past week and i've been having to put out frozen water bottles and have been misting the rabbits. We are going away for a few days and i have a friend that is going to be coming over twice a day to care for them and the babies will either be born when we are gone or just before. I am concerned the babies will be too hot in this weather with all the hay and fur in the boxes covering them up. I could move them inside but it is a last resort and will probably stress the expectant mothers, not to mention they make a huge mess in our bathrooms and the pet sitter will not be happy cleaning up mounds of poop from the floor as neither is litter box trained. I can move them inside but would rather have them left outside if they will be okay. Does anyone know what would be safe for the babies? (We are planning to get both spayed but we don't have any male rabbits and they got pregnant from being out in the yard when a neighbor's male rabbit dug under the fence.)