Exactly how steamy is this story?
PG-13
Holly Black calls the book "funny, dark, and sexy" (source). It's definitely all three, but like the magic, angels, and demons, hiding in plain sight in New York City, the sexiness is shimmering below the surface.
There's only one allusion to sex in the entire book, and it comes from Clary in a fit of jealousy at seeing Simon dance with Isabelle: "If they dance any closer together, they won't have to go off in a corner to have sex" (12.64).
Clary does ogle a lot of cute boys, but what fifteen-year-old doesn't? Once Jace shows up though, he has all of her attention (well, at least his hard abs and swelling biceps do). But he, and everyone else, remain clothed for the majority of the novel. The most skin you're going to get from the book is on the cover. Jace wears a gauzy, semi-transparent shirt in a dream sequence that shows off his bad-boy tattoos, but that's about it.
As for actual physical contact, Clary and Jace do share a couple of steamy kisses, but that's before they find out they're related. Yes, you read that right: Clary's making out with her brother, but that's all they're doing (thank the Angel).