Unlike Shouto Todoroki and Endeavor, who can actually somewhat control their flames, (Y/N) Todoroki can't.
Their flames are different. At first they thought they could just heat and cool their hands, but one day while in an argument with their cousin Shouto, they discovered other wise. "You're just like father!" Shouto said. "No. I'm not." (Y/N) said stern and angry. "Yes, you are!"  Shouto shot back. "NO IM NOT!!" (Y/N) said as their hair, eyes, and hands burst into blue flames. You shared your uncle's temper, but unlike Shouto you didn't have a handle on it. (Y/N) stared in shock and fear you started crying and ran away from Shouto. That was when they were 6, it's been eleven years since then.
(Y/N) has since learned to better control their quirk. Their quirk allows them to control the temperature of the flames, it can change from being charing hot, to warm enough it can't burn, to even so cold you'll get frost bite from simply being near it. The one problem is that it tends to... 'flare' up accordingly with (Y/N)'s emotions. Like when they're angry, sad, embarrassed, stuff like that. Ever since the incident with Shouto, they haven't seen each other. So how were you to know that he was going to U.A.? Or that you'd both be in the same class? You couldn't; until you walked in that is. There was a sudden dead silence in the room when I entered, yeah, you were new, but also because of the pure shock on your and Shouto's face when you made eye contact.