Crazy, crazy! Sure hope they survive – do you think you need to put insulation around the box to keep it warmer? You would just put the foam directly against the wood, not with spacers like you do when trying to keep the heat OUT. I have done this before when I had eggs, not babies, and it turned unusually cold. I even wrapped the foam in plastic to keep it warmer. If I remember correctly, they did survive a pretty cold spell, eggs that is, not babies. Best of luck.
We had temps in the upper 20’s the past few nights, but tonight is supposed to be just above freezing and then warm up some next week.