No, unlike us, birds do not have sweat glands.
When we work outside on a sweltering hot, humid summer day, within minutes our skin and clothing are wet with sweat. Sweating helps keep us from overheating.
Since birds do not have sweat glands, they must rely on other means to keep their body temperature from reaching dangerous levels. One of the main ways they are able to accomplish this is by panting.
If you closely watch the birds moving about your backyard when temperatures soar, you are apt to see one or more pant. When a bird is panting it holds its bill open longer than it normally would and increases its breathing rate. This greatly increases the flow of air across the moist, warm surfaces of its respiratory tract. This helps dissipates the bird’s body heat.
As you might expect, you are most likely to see this behavior during the hottest parts of the day.