My daughter lived in a small apartment when she was going to college. This was in an older neighborhood where they had a lot of mature trees.
The apartments did not have central air, and the residents could put in portable room air conditioning if they wanted to.
My daughter thought she would try to go without it, but it was much too hot. It can be hard to study and focus when you are sweaty and irritable.
My husband installed a window air conditioner for her which cooled off her whole apartment. One important thing is to make sure the weather stripping is tight around the unit. This can really help keep the hot air from coming through any cracks.
When she moved into her next place that had central air, she was not sad to give up her window air conditioning. Central air is more convenient and much quieter.