Summer baby

Ok this is probably a dumb question but I'm really struggling trying to figure this out lol. My baby is due in June so she'll be a summer baby. So at night what do you dress a summer baby in? It's going to be cold in the house with the air conditioning on, but she can't have any loose blankets. Do you put them in a long sleeve cotton zip up pajamas or will she be too hot in that? I know they can't regulate their temperature so I don't want her to be too hot or too cold. I have the shorts pajamas but will she be chilly at night? Help a momma-to-be out please 🙏🏼