You're right, heaters are not needed during the spring/summer months that's why we don't put them in during the warmer months.
Even in the middle of winter (when we do have a heater in the unit), it keeps on the warm side since it's a concrete structure and gets direct sunlight all day.
The doors you're referring to outside of our unit, are NOT storage spaces. They are utility access chutes...for the cable companies, maintenance etc; and they are supposed to remain locked otherwise.
I will report them to the bldg. maintenance department.
As far as the A/C, we list it on our AirBnB page as NOT including an A/C unit.
We have actually had someone look into installing one for us, but the models that could be installed (in any of the units) are not very efficient: the 'mini-splits'.
But again, that would only be used in the hotter days of summer, since we have a pretty strong ocean breeze blowing pretty steady most of the time; and we also provide fans. There are two fans in the unit, and we bring another one in (pedestal fan) for the summer months.
We don't keep it in there in the spring, because, again, most guests do not need it then, but it's available upon request.