Harry Potter was a highly unusual boy in many ways. For one thing, he hated the summer holidays more than any other time of year. For another, he really wanted to do his homework but was forced to do it in secret, in the dead of night. And he also happened to be a wizard.
Non-magic people (more commonly known as Muggles) were particularly afraid of magic in medieval times, but not very good at recognizing it.
On the rare occasion that they did catch a real witch or wizard, burning had no effect whatsoever. The witch or wizard would perform a basic Flame Freezing Charm and then pretend to shriek with pain while enjoying a gentle, tickling sensation. Indeed, Wendelin the Weird enjoyed being burned so much that she allowed herself to be caught no less than fortyseven times in various disguises.