He should be fine. He might not be happy, but he will be fine. He can bask if he gets cold. Don't be surprised if he's slow and doesn't want to eat. If you can get a larger bulb wattage, that might raise his basking spot up a few degrees.
The super deep cold should ease up soon! It was -27F when I left KC yesterday morning. It's -11F in Saskatchewan right now. Fun!