Since cats don't pant like dogs how do they release trapped heat?

Cats do pant, but also run hotter and enjoy higher temperatures than humans (24-26 °C depending on race).

Also, cats have lots of ways to release heat, cats can arrange their fur to release more heat (or burr it to trap more), they lay on cool ground, they can lick themselves for evaporative cooling, and of course seek shade when it gets hot.

We had a hot summer with temperatures of over 30 °C indoors and I got worried my European shorthair would overheat, got them a gel pad that wicks away heat when laid upon, but they thought it was ridiculous and just laid on the concrete floor in the shade whenever too hot and was super comfy and lazy.