Are cats supposed to pant?

The answer is yes, under certain conditions. They are supposed to pant when hot and/or stressed or frightened.

Panting is a normal event after exercise for example. My lady cat pants when she travels in the car. She gets agitated and overheats a bit and starts to pant. This is only moderate but if a cat pants excessively and if it is labored watch out for heat stroke.

Panting lowers the cat's body temperature. Water in the mouth, on the tongue and in the lungs evaporates and cools the cat. The cooling effect comes from the process of the latent heat evaporation.