Interesting question. My hunch is that he is too proud to coach somewhere else and confront that he got fired from his 'heart' school. It meshes well with his delusional assessment of his own success - or lack thereof at times. He is also an approval addict and deeply desires the acceptance of the 'people'. That's coupled with the notion that he is a pretty good guy, cares about the players, and wants to do things rights, i.e. good guy.
Thus, based on this personality, I'd say he will figure out a way to say he's coached long enough, loves the school, and while he doesn't want to coach anymore he'll stay a Tennessee guy a la Pat Dye at Auburn.