"You'd better bring your A-game every week," he said Saturday night in the Neyland Stadium press box, "because it's not far from the penthouse to the outhouse."
Tennessee fans hope that's true because the Vols seemingly have a long-term lease on the outhouse. Since Fulmer was fired for going 5-7 overall and 3-5 in SEC play in '08, successors Lane Kiffin and Derek Dooley have combined to go 21-24 overall and 8-20 in league competition over the past three-plus seasons.
The obvious question: Will the Vols ever get back to the penthouse?
"Absolutely," said Fulmer, who was honored prior to Saturday night's Tennessee-Alabama game. "We've got too great a history and tradition and facilities (for it not to happen)."
Fulmer's optimism is based on solidarity. He believes school administrators are collaborating to rebuild a football program that has been in shambles.
"I think everybody's working much better in the same direction," he said. "For a while we were splintered all over the place. I think Derek is doing a good job and I think (athletics director) Dave Hart is trying to get everybody focused in the right direction.
"You've got a collection of really bright people, people that love the university — chancellor, president, athletics director — and they're all pulling to get the same things done ... campus-wide but athletics especially. So, absolutely, I think we can get back to where we've been."
Fulmer isn't ready to give a timetable for Tennessee's return to relevance just yet, however.
"This league is as tough as it's ever been," he said. "Missouri and A&M will have something to say about who goes to the next level, up or down. The same thing happened when we went to divisional play: It separated the real men from the boys."
Tennessee hasn't been one of the SEC's "real men" since Fulmer's 2007 team capped a 10-4 season by beating Wisconsin in the Outback Bowl.
Although the league has swept the past six national titles, Fulmer suggests the SEC is no tougher now than it was in the 1970s, '80s and '90s.
"It's always been competitive," he said. "Now there's six ranked teams rather than five or seven rather than six (due to the addition of Texas A&M and Missouri). What's going on in this league is the same thing that was going on in the '90s."
During his halftime interview with nearly a dozen reporters Fulmer was asked how tough it is for a school to recover after making a coaching change and choosing the wrong successor.
"I don't know if you're referring to my situation or just period," he said, "but there was an awful lot of good chemistry and stuff (during his tenure) that went a lot of different ways. We've got to get all of that pulled back together. Winning helps a lot of things."
With the 2012 Vols off to a 3-4 start that includes an 0-4 record in SEC play, Dooley is feeling some heat this fall. Fulmer can relate. He felt some pressure when his 1994 team staggered to a 1-3 start.
"Doug Dickey (athletics director) and Joe Johnson (UT president) and all of us were pulling in the same direction and we turned it around, won seven of the next eight, including the bowl game," Fulmer recalled. "More importantly, that laid the foundation for the best modern era of Tennessee football after that (a 45-5 record over the next four seasons).
"That's what we need to do: All get focused on pulling in the same direction and have a big win somewhere that makes a difference to get us going in the direction we want to go."
Having served Tennessee as a player, assistant and head coach, Fulmer was understandably thrilled that his alma mater chose to honor him and his 1997 SEC championship team Saturday night.
"Today was really, really special — to share with my family on the field and then my extended family, the football team, and especially with that particular class," he said. "That '97 class was kind of the foundation of a lot of what we accomplished here.
"I think they were the No. 1 recruiting class in the country in '94, and it turned out that we won an SEC championship with 'em. Really, a lot of those guys were part of the '98 national championship game.
"I'm very appreciative."