The 'Hot Tree Guy' might be a character who is introduced to add an extra layer of intrigue or a love interest. He could be someone who catches the attention of the main characters, like Bella. For example, he could be a guy who works in forest conservation in Forks and has an uncanny ability to sense the presence of the supernatural beings in the woods, which makes him both alluring and dangerous in the context of the Twilight - inspired fanfiction.
There's also a possibility that the 'Hot Tree Guy' is a misnomer or a very specific reference within a particular subset of Twilight fanfiction. It could be that in a certain fan - created storyline, a character is given this nickname because he is often found near trees, perhaps he has a special power related to them, or he just has a habit of spending a lot of time in the forested areas around Forks.