The purpose of a protected structure is to keep the heat out.
If that is effective, then the outside air will be much hotter than the air pulled in.
In the case of a cooler, even if it does work, you will be cooling outside air, also ineffective.
Solar chimneys have been used to generate electricity though.
You want shade separate from the interior to use ventilation between the upper and lower surface.
Failing that possibility, a chimney will ventilate a van, etc when the inside is warmer than the outside air.
Painting it black should be enough, though using a clear tube around it should work.
Bigger is better, taller is better.
It is possible to have too big an intake, due to the venturi effect.http://en.wikipedia.org/wiki/Stack_effecthttp://en.wikipedia.org/wiki/Solar_chimneyhttp://en.wikipedia.org/wiki/Windcatcher