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Most (not all) established chilli plants can survive 5°C nights. In my experience they don't really like it though, above 10° is better.
Freshly pricked seedlings I'd pamper a bit more, bring them inside at night, and gradually let them get used to the colder temps outside (leave outside one night, bring back in the next two or three, one outside again, bring inside one or two nights.. and keep the plastic greenhouse things you have on for the first weeks as well).
Godspeed!
Pricked out my seedlings yesterday. If I'm keeping them in a plastic greenhouses would it still be advisable to bring them in overnight?