They release heat however they want and whenever they bloody-well feel like it.
Basically, they breathe with their mouths open, which becomes panting when necessary...
A common cooling mechanism, cats will breathe with their mouth open and tongue out, accompanied by heavy breathing noises, when they're too hot. As the heatstroke worsens, the panting will increase. Panting is a perfectly normal response to overheating and should begin to subside as your cat cools down.
I didn't mean specifically when they are in a crisis state of overheating. Dogs have their tongue out whenever they're doing anything, which I assume keeps them from overheating in th efirst place. Cat's don't.
House cats descend from African wild cats. Desert creatures well acclimated to high heat environments. In cooler climates the cat's main priority is staying warm enough rather than cooling down. Which is why my cat is presently curled up with her nose in her tail trying to stay warm with my air conditioner maintaining the house at 75 degrees.
Dogs are descended from wolves. Arctic creatures well acclimated to cold environments. So they spend most of their lives with their mouths wide open and their tongues hanging out.