Cheffy, go for it if you want it. The school should know both of you well enough to make the right decision, and their right decision will probably be the one that is best for their students. And that's for the greater good.

Before you throw your hat in the ring, though, make sure that you can handle it emotionally if they choose the other guy for the full-time job.

I spent 30 years in corporate America, where you always knew you were competing with others for promotion. The guys who treated this competition like it was tennis sometimes won in the short term, but lost in the long run because they lost the ability to be team players and had become politicians. The guys who treated it like golf, where you compete against the course, not your fellow competitors, always won in the long term.

If you get the full-time position, don't gloat. Meet with the other guy privately and offer him your support to get the next full time position to open up at your school or elsewhere. Worked just fine for me!