Depending on the size of that door, you could replace it with a security screen door - that will add a lot more air flow, especially if you've got a window/sizeable vent across from it. We added a livestock fan opposite our metal security screen door and it made a tremendous difference - if you do a fan make sure it's made for the abuse of chicken dust/dirt that will kill most fans and can turn them into fire hazards.
https://www.valleyvet.com/ct_detail...itemguid=fb6cb6e4-8b91-4df5-ad8c-f8b5055fe291
https://www.valleyvet.com/ct_detail...itemguid=fb6cb6e4-8b91-4df5-ad8c-f8b5055fe291