The voice of experience...d:o)
We put a screen door on that bedroom years ago when it became the kitty nursery. We have window A/C units, not central air, and a screen door was the only way to keep the room cool in the summer. Kittens usually stay in that room until they’re about 3 mos. old and they get to meet the others through the screen. No problems with anyone being mean to them when we let them invade the rest of the house. LOL