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If you have a smaller hole somewhere, hopefully on the backside of your garage you could try a portable AC unit. You didn't say if your garage was attached or detached. My detached garage backs into my backyard so I can get away with stuff the HOA would not approve of.. i.e. Window ACs or holes in my garage.

Something like this.

https://www.lowes.com/pd/Hisense-Hisens ... 5000151929

It has a round hose on the back to exhaust the hot air. Obviously, with a 3 car garage, you are fighting a big heat load. Your problems will be insulation, leakage around garage doors. output and expense of the unit itself and if you are in a high humidity environment you will have to drain or empty the unit's moisture collection system.

I had a large one, about the size of four of these units from a server room that I decommissioned. It kept most of my garage cool while I was using it. The problem is the initial cost if I had purchased the unit was 8k and the exhaust tube was about 30 inches in diameter. So it worked okay for a while until I just gave up. Oh, and the electricity was ugly. Cost about 60 bucks a month to run it half a day. So in the long run I decided to give up. My problem is my garage has zero insulation.

Something like this version. The exhaust port is on the top and requires a very large hose to connect to the outside. Prices have come down but this one is still about 2000.

Good luck.

https//www.amazon.com/dp/B01AAAY1ZO?tag=aclabn ... th=1&psc=1