any advice on cooling basement for a cat?

Hello. Im in need of some advice. About 6 months ago, I took in one of my stray cats, Lola, because she had showed up one evening with an injured paw. she was bleeding and limping so i didn't think it was safe for me to leave her outdoors. I have 4 indoor cats of my own and because i live at home with my parents and siblings, i couldn't just bring her in the house. My parents have never objected to my caring for strays and they actually provide financial assistance as much as possible but as far as taking in more cats, 4 is their cut-off.  my dad is a small business owner and his store has a basement, which is pretty clean. since i had no other option, i took Lola to the basement, which has a decent sized finished room. my brother was using it to do his studying there but he gave up the room to Lola.

Lola has since healed, shes gotten spayed, vaccinated, all the stuff cats need but she still hasn't found a home. she's all black and im sure that has something to do with it. at this point, im not sure i even want to give her up. im supposed to go away for grad school and im going to take her with me. but right now we're still in my dad's basement. i stay here with her, only leaving her to go to class or home to sleep. i do all my studying here rather than the library, which is perfectly fine, as this allows me to care for her also.

the basement is very spacious but it's not finished. only the room is. my dad uses it for storing his inventory, like sodas and bottled beverages and water mostly. since i started hanging out here, ive been keeping it even more clean for Lola's sake. I clean the room that she is in twice, once when i come in and before leaving. the floor is tiled so it's pretty easy to clean the room. the basement has an exhaust fan in the window which gets turned on in the summer months. the room where lola and i stay in also has a small window but it doesn't open to the outside, but rather to the other part of the basement. it's situated in an advantageous area - when the fan goes on, the room gets cooler. the basement has no leaks. when i leave at night, i do close the door to the room because i don't feel comfortable giving her a free reign of the basement. im afraid she might get into something and i wont be able to get to her in time. the store is 24 hours so there's always someone upstairs. the door to her room is never locked and i come in the morning to let her out and feed her before going off to class and returning later in the day.

the winter months were not bad at all but im worried about the summer months. when lola and i first took up residence here, it was october. i remember feeling very hot and frustrated at times but then in a few weeks time, the weather changed and we were ok. i don't know what we'll do now that the weather is warming up rather quickly. i live in nyc and temperatures are consistently in the 50's now. as a human, i can take many actions to cool myself down and i still have a home to go to at night, im worried about Lola. i don't know what to do. it's going to get warm. my sister keeps telling me to give her up and i know my parents probably want me to do the same, but i can't give her up. it's probably not very practical for me to act this way but i can't be without her.

what can i do to keep the basement room cool in the coming months? i can't install an ac there - my father would never agree to dealing witht the cost associated with running it. it's not bad at all right now but things will change fast and i need to do something before that happens. the distance between the room window to the other basement window is about 40 feet. ive thought about leaving the door to the room open in the summer and just let her walk around, but i'd probably have to make sure there's nothing hazardous that she can get into.

this is not a permanent home for her. i do plan on taking her out just as soon as i can get my life in order. i don't have that many options right now because im a student and i am unemployed.

thanks!

your suggestions are appreciated

The basement should stay a relatively constant temp because it is underground.  The fan is needed to move the air, so it doesn't get stuffy.  Have you been down there in summer and know it gets too hot?

If so, they have room air conditioners that need window access but that do not need to be in a window.  They have long tubes that exhaust to an outside window but that allow the conditioner itself to sit on the floor of the room.  Not sure how close the nearest window is but you might be able get an extension ( the tube similar to a dryer vent hose).

Thank you for helping her!