Cats do pant, but they’re also just better adapted to heat than dogs are.

Smaller frame means less body heat to disperse; As size increases, the volume:surface area ratio heavily skews towards volume. More volume means more trapped heat. By minimizing volume and maximizing surface area (skin) cats are able to effectively stay cool passively.

Cats also have a higher basal metabolism, which means their body temperature is naturally higher. And creatures don’t feel heat in an absolute sense. Temperature is felt relative to your own body temperature. That’s why a warm shower after swimming feels downright scalding, (because you’re cooled down from swimming, then hopped into a warm shower,) or why the regular room temperature bedroom feels chilly when you have a fever (because you’re warmed up from the fever, so the room feels colder than it normally would.) You’re feeling those things relative to your own body temperature. Since cats have a higher base body temperature, they feel warm environments less than we do. This is also why they spend so much time lazing around in patches of sunlight, or snuggled up next to the radiator; Room temperature is comfortable for us, but slightly chilly to them.

Third, they are originally adapted from the desert. This means they also have some quirks, like tolerating high temperatures better, and having a high tolerance for thirst, (the latter often leads to kidney issues later in life, since cats don’t tend to drink enough water even when it’s readily available.)