I was wondering this as I considered how effective panting would be for humans as a means of cooling.
This article quotes a professor of respiratory physiology that says "dogs are built to pant just right. The mechanics of their lungs and chest set a precise rate for panting that minimizes the amount of work while maximizing cooling power." They also don't breathe fully when panting, so they can still cool themselves without increasing gas exchange. This is different than humans, who will hyperventilate to get rid of carbon dioxide (or you can intentionally hyperventilate and cause respiratory alkalosis).
Not knowing the physiology or the literature, I can say based on personal observations that dogs, even when extremely hot or exhausted, mix in a routine of deep inhales and exhales to their panting. Perhaps this prevents unwanted side effects of their cooling mechanisms.
Our physiology is quite different. I guess their larger surface-area tongue is one obvious difference, and the fact that they have limited sweat glands. I actually thought they had none, but this article states that they have them on their feet.
Another fun fact there is that they don't just use panting -- they can apparently constrict/dilate vessels in their face and ears..