It's quite unlikely that any tarp would keep the eqq as cool as an a/c would because it actually removes heat from the air and also dehumidifies the air. All a tarp can do is bring the temperature down to shade temperature.
In my case, what I was looking for was to keep the eqq from being heat-soaked in the direct sun because then the insulation works against you and keep the inside warm for a longer time at night. I was pleasantly surprised to find out that it kept it pleasantly cool during the hot days also when I used it in the open at Black Canyon of the Gunnision River NP later that Summer. As I said, I have also had good performance from a tarp over the egg on a rope between two trees, but that isn't always an option.
BTW, in the Boler
photo it looks like the shorter poles are PVC and the longer ones are metal.