Yes. That is what I was thinking about.Make your own stip door. Take an old pillowcase or similar and cut strips most of hte way up, tack it over the door. Presto-chango - your own strip door. Will help hold some heat in and act a bit as a baffle for windier nights
The door is low down so doesn’t contribute to drafts - but it would probably still be warmer with something like that.
I made strip curtains for the big nest boxes using an old vinyl tablecloth.