How did Professor Quirrell shake Harry hand in the Leaky Cauldron when he touch without being burned?

In the Harry Potter series, Professor Quirrell did not shake Harry's hand in the Leaky Cauldron and touch him without being burned. That event in the book occurred when Harry shook hands with Hagrid, not Professor Quirrell. Here's the corrected context:

In Harry Potter and the Philosopher's Stone, when Harry first met Rubeus Hagrid in the Leaky Cauldron, he was surprised that Hagrid's giant hand didn't burn him when they shook hands. Hagrid explained that he had been expelled from Hogwarts School of Witchcraft and Wizardry for something he didn't do, and as punishment, he was forbidden from using magic. This meant he could not use protective spells or charms that would shield him from touching certain objects or people that might otherwise cause him harm, like Harry.