Air conditioner or no air conditioner for baby?

Jeanette
This is something my boyfriend and I argue about every single day. We live in southern california, where its been 100+ degrees everyday, today its 105 . Our house is extremely hot because theres no trees or anything around us. The only a/c we have is in our bedroom in the window so im in there all day with our 1 month old . My boyfriend says babies are supposed to stay warm and shouldnt be in the a/c. When he takes care of him, i get him back so sweaty on his back and head. I tell him all the time about SIDS but he thinks he is right . Who is right/wrong here?