I would cover the cage on 3 sides and crack your window open. I have heard that Budgies have night freights so that is the reason I say to leave one side of the cage open and have a small night light in the room for it but maybe someone here knows better then me. If you are talking about it getting really cold, like below 65 in the night you can purchase a bird heater to hang on its cage. My daughter has one and her Conure loves it in the winter time when it gets cold here. She plugs in the heater and covers his cage and he snuggles right up to it. If you find another heater just make sure it is bird safe because lots of heaters have Teflon coated parts and Teflon lets of toxic gases that kill our sweet birds. Tikki my daughters Conure has this heater in his cage and he really does love it.
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