You should be able to install a damper to isolate the vent when you don't want or need it. If the location is easily accessible, a manual damper should do the trick. If not, consider a motorized damper.

The HVAC system for your garage should be completely separate from any system that supplies conditioned air to the living area of your home. We've installed mini-split heat pumps to condition garages and they work well in our (coastal Virginia) climate.

Thank you for responding! Yes, the garage is completely separate from the house.

I tried one of those turbine fans in my attic, and it INCREASED the temperature rather than lowering it. What was happening was the turbine removed hot air from the attic, creating a vacuum. The vacuum then resulted in air being pull in through the vents on the roof. But super-hot air was coming off the heated shingles and entering in through those vents. The result was that hot air was being replaced with even hotter air. If you have no roof vents and instead just take air in from soffits under the roof, it might work better.

You might want to consider a radiant heat barrier on the inside of the roof in the garage, and then use the heat pump for active cooling. When the outside temperature is lower than your temperature target inside, you could turn off the heat pump and switch to the turbine (again, assuming the vents that the turbine is helping to pull air through are underneath the heated shingles).