Short answer: Yes, & you should be able to make this work too.
When I lived in the desert, I had a "swamp" cooler* installed on the roof of my garage (that was attached to my house). *You have plenty of humidity, so
you'll need a regular A/C (which unfortunately costs more to run than a swamp cooler). My cooler was controlled by thermostat.
The cooler down-drafted into the approximate center of the garage (a huge 4+ car garage, btw- if yours is smaller, it won't take as much to cool), & I also
had 4 "up-ducts" installed, so that when the cooler ran, the stale warm air rose up & out of the garage. This kept the odors out of the attached house very
well. The up-ducts automatically flap closed when the air wasn't running, so in the winter the warm air stayed in. I used the garage for my one vehicle at
the same time too, but it wasn't opened frequently...just when I came & went to work etc. (My garage was 'fininshed'- ie. insulated, even the door.)
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