Make my own dropdown ceiling

[stuckinfl]

I moved into an apartment that gets real got. It's a flat roof building, I'm on the second floor on top of stores. It's actually a neat place and cheap too. But when you stand on a chair and touch that ceiling in the late afternoon, It's hot! I did put in a new AC which helped, the old wall unit was 20 years old. But I had another idea. The ceiling is over 9 ft in this studio apartment. What if I built sort of a makeshift drop-down ceiling that reduced the air volume in here and provided a barrier for the heat. Like an attic does. I could build out a framework with wooden strips and then lay some kind of insulation board or fiberglass on top of the wood. Do you think that would make a difference? Another option is I could buy a huge piece of fabric that's air resistant, like parachute material. Then just string it up and let it hang down about a foot.