I have peppers at transplant size, and also an Earth Box with peppers bearing fruit right now. I cover them up with a frost cloth tent if the temperatures are predicted to go below 50deg.
That said, our humidity is probably a little higher than yours so just be sure your transplants are well watered if they're going to be out on cold nights for a while. But just water the soil, don't wet the leaves if you water them in the evening.
