Great observation! And great question! Birds do pant to cool themselves! As you can imagine, birds can’t sweat, so panting is a good way to get rid of excess heat. Panting increases evaporation across moist surfaces, such as those found in the mouth, throat, and lungs, and helps cool the body. Some birds do “gular fluttering" (rapidly flapping the membranes below the bill to increase evaporative cooling), but that type of thermoregulation is mostly seen in non-passerines.
Here are some photos I have of crows panting on hot days:
valleah asked: today I spotted a crow walking on a well manicured lawn looking at all sorts of things with his beak wide open the whole time. it was fairly warm here (upper seventies, Fahrenheit) is this something they do when they're hot?