We have a geothermal HVAC and the main exchanger unit is located in our conditioned crawl space (concrete floor/closed cell foam on 4' concrete stem wall and rim joist) so the underside of the homes floor joists and duct work is easily accessible.

The duct for the FROG room comes off the main trunk line in the crawl and the booster fan is located near the beginning of the duct for FROG room.

The HVAC vents are located in the ceiling of the FROG room so vertical heighth from fan/main duct in crawl to vents in ceiling is probably close to 20' and length of duct from start of duct to middle duct in roon is probably close to 35'.

The fan does not make a huge difference in the force of air blowing out of the duct but it does make a big enough difference to keep the FROG room almost the same temp as rest of the house year round. With geothermal we are able to keep our house temp at 69 in the summer and without the fan running it was probably close to 80 in the FROG so we easily had a 10+ degree difference by using the little booster fan.
If you try this route hope it helps

Try leaving the cars parked outside the garage until they cool down and then move them into the garage. This can cut down on the heat considerably.

There's 2 schools of thoughts on insulating a garage. Some say if you're parking cars in there on a regular basis it hurts to do so as it's keeping the heat IN rather than letting it dissipate. In this instance I think an exhaust fan near the ceiling set on a thermostat would probably be best to get heat out of the garage (provided you have vents to the outside down low like you should to let Carbon Monoxide out.

The other is to insulate it and the heat will eventually work it's way out.

The heat gun makes a whole lot of sense to see where the heat load in the room is coming from and perhaps can insulate better to help with that.