If Jon Snow is a Targaryen, why did his hand get burned? Is it because he is half Targaryen?

Targaryens are not impervious to fire. In fact, during the Dance of the Dragons, at least two Targaryens died from fire related wounds. In the books, Daenerys has all of her hair singed off due to dragon fire. The television series, I have a feeling, is written by people who are not book readers. I am sure that they have some kind of outline or rough copy of the finished books, but the finer details are occasionally overlooked. The show will get it right in the end. It may be frustrating for book readers, but part of the problem is GRRM has not released the final two books. Most people are forgetting that Viserys was burned to death with molten hot gold in season one, which makes Daenerys seem somewhat ridiculous to attentive watchers.