Why don't cats have to pant?
Transpiring and panting are ways to regulate body temperature. When sweat evaporates, it cools the skin, and panting releases heat through the mouth. Horses, humans and even plants transpire for this reason, while dogs and birds pant. But how do cats release heat?
In fact, cats sweat through their paws. It appears that a cat after it has been frightened may leave wet pawprints on the floor. Although it's all over the internet, I couldn't find a convincing picture and as a cat lover, I've never noticed this phenomenon. That aside, cat's paws have little surface area, and cannot provide much cooling power. Instead, felines have other, more effective strategies to adjust their core temperature. Like dogs, they often sprawl out on cool surfaces (Fig. 1), or they seek out the shade on hot days. They also tend to sleep a lot, which reduces core temperature and is preferable of being very active in hot times in terms of body temperature (Fig. 2).

Fig. 1. Sprawling cat. source: Columbian blogs

Fig. 2. Cats in the shade. source: Cat memes
Source
- Indiana Public Media