Is this a dealbreaker?? (no central AC in my boyfriends house) (description below)

I grew up in a nice decent house with my dad and sister. And since being an adult and having my own apartment ive always had air conditioner and like to sleep with it cozy and enjoy being able to adjust the temp. Well, ive been dating my bf for almost 2 years. I have a 2 1/2 year old son who is used to sleeping with the AC/ cool air on him. I live in SoCal so its very hot. Well, me and my son are moving into my boyfriends house in a few weeks which has no AC or heating system. To save money and not have to pay for rent and to begin a new chapter with my boyfriend. Well he has those AC units in the windows and it keeps each room very cold. But he has no central AC system. It costs thousands and since its a temporary house for him/us, he would rather not get that and just save that money.

I dont know. Im scared for just this life change and i wonder how my son will react to no AC. Relaxing in the living room might involve some sweating. Yes there is an AC thing in the living room window too and a fan in there. But it will still maybe get hot. Its just not in as nice of an area that im used to. It is a safe neighborhood for me and my son.