I’m sure this has been discussed before, but I’m not even able to get the right search terms on Google, so GQ it is.
What I’m wondering is, which is the cheapest way to cool down a car - opening the window, or using the cooling fan?
The alternative would have been to search Cecil’s columns first.
Start with a white car, which will not take on as much heat.
Ah, but that column is from 24 years ago, when the bestselling car in the U.S. was the Chevrolet Celebrity - surely aerodynamics, cooling systems and research in this critical field has advanced since then?
A local paper just did an unscientific test on this; i.e. one guy and two weeks of driving to work and back. There was no perceptible difference between driving with the A/C on or driving with the windows down.
YMMV
Don’t you, like, live in Canada, Leaffan? Because I don’t think that’s really a useful test.
Mythbusters also addressed this. Their drive test gave the edge to windows down even though a computer model had favored A/C.
Either way, we’re talking fractions of mpg. You can probably save more gas through non-aggressive driving and keeping your tires inflated.
Okay, I took the question to be addressing not just fuel efficiency but also actual cooling. Did you mean it that way or not?
What I do is drive with the windows closed and cycle the air conditioning on and off. You can’t just turn up the temperature, because that runs the compressor full time and meters in warm air to adjust. You’ve got to run the AC full blast until it’s too cold, then turn it off until it’s too hot.
The type of car you drive is going to affect this too - size of windows relative to cabin area, size of engine (and thus proportional amount of power used to run the compressor on the AC unit).
I doubt it makes much difference unless you drive a car with a lawnmower engine and like the temperature in the cabin to be close to freezing, and you don’t open the windows before setting off to clear out the hot air.
You think we never get hot weather here? 
I had heard that there was a Lamborghini ad back in the 70’s or 80’s that made the claim that they got better gas mileage with the A/C on than with the windows rolled down because they were so aerodynamic (haven’t been able to find it now-- maybe I’m thinking of the wrong supercar). This was back in the days of huge A/C compressors and brick-like styling, so getting better mileage with it on would have been unheard of-- it sounds like these days with much more efficient A/C units and more aerodynamic cars it’s more of a toss up.
At highway speeds windows up/AC on will give you the best fuel economy. Low speed city driving, windows down/AC off is better.
You could always get a ClassicAire Car Cooler. Depending on your vehicle, it would definitely be “cool”, but I don’t think it would help your gas mileage.