The study room gets no AC

My brothers obtained a fixer upper house & they system to flip it, and everyone in the family has been going over to the house to help replace it, the room I have been focusing on is the study room.

The study room had a popcorn ceiling & wood walls, however it looked absolutely ugly.

The first thing I did was scrape the entire ceiling. I then sanded the wood walls, put a sealant on them & painted on top. The next thing I am toiling on is painting the ceiling. I think it is going to take various coats & I need to be careful around the wood beams & not get paint on them. The ceilings are absolutely tall & peaked. I have to be strategic where I put my ladder, however of course I am doing the painting in the Summer too. The outside temperatures are in the 90s & heat rises… My brothers swear they had the cooling unit on & running. I can’t hardly suppose anything when I am on the top rung of the ladder stretching to paint. I have sweat run down my face, legs & tummy. I have to be absolutely careful with hydration or I might pass out, and what is not good is that this is an air vent way up high. The air vent technically should allow A/C to hit me directly in the face. Either there is something wrong with the HVAC duct or the AC, but I don’t suppose a thing. The study room is always toasty hot. Eventually my brothers need to fix this or have the house shown in the winter.
Geo heat pump