This story takes place before the events of Kingdom Hearts and Kingdom Hearts II.
It is also considered an alternate universe.
Heat Blur takes place in the world of the Sonic the Hedgehog videogames, which will be (incorrectly) dubbed Mobius during this story. It is set during Sonic the Hedgehog 3 and Knuckles, approximately six years before the events of both Kingdom Hearts II and Sonic Next Gen.
This is a fan interpretation of both Axel's character and the events in S3&K. At the point of writing this story, extremely little is known of Organization XIII, so much of the information about the group and it's motives is completely speculative.
A final note, no claim is laid to the characters, locales or basic storyline within. Sonic the Hedgehog belongs to SEGA, and Kingdom Hearts to Square-Enix.
The story begins late one night in a silent rainforest, where the newest member of Organization XIII has been left to his own devices.
The elders of the Organization considered themselves unable to spend time training their youngest members, so instead they sent them off to a random world without explanations or guidance, and let them figure it out for themselves.
Axel, as he has been newly renamed, is more than a little lost. He has absolutely no idea what's going on, and is more than a little puzzled over the fact that he now seems to possess a tail. Saïx had tossed him out of a portal of darkness not ten minutes ago, and Axel's confusion was exacerbated by the fact that the absolutely wonderful number VII had thrown him face first into a tree.
So far, Axel was unimpressed by his new bosses.