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Fulmer was the guest speaker at the Knoxville Quarterback Club on Monday at Calhoun's on the River.
It was his first time speaking to the club since Dec. 1, 2008, two days after capping his UT career with a 28-10 win over Kentucky. Fulmer was fired with three games remaining that season.
"I'm standing here as a fired football coach and I have to figure out a way not to put Derek Dooley in any kind of a bind and answer your questions,'' said Fulmer, a first-ballot selection into the College Football Hall of Fame in May. "I see those cameras back there, and I don't want to end up on (ESPN) SportsCenter.''
Fulmer, 152-52-1 with five appearances in the SEC championship game during his coaching tenure from 1993-2008, likes the direction Dooley has the No. 23 Vols (2-0) headed entering their game against the No. 18 Gators (2-0).
"I'm glad to see where we've come, and the attitude that's prevailing now; everyone is excited about Tennessee football again,'' Fulmer said. "It's been a fun team to watch, it looks like there is progress on both sides of the football.
"There's a lot of reason for optimism for what we're doing,'' he said. "I think they (Florida) are vulnerable. I think it's a good time for us. The stadium will be packed, and the frenzy will be back.
"Now we have to handle that in the right way.''
ESPN's College GameDay will be in Knoxville for the first time since the Vols lost to Auburn on Oct. 2, 2004. Tennessee won the SEC Eastern Division that season.
"This game's not the end of the world either way — make sure you write that — but this is a big game,'' Fulmer said. "There's a lot to be learned and proven by this particular team, but they've got some skill, and it's an exciting team.
"It seems (Tyler) Bray has matured in how he's handling himself on the field and in the offense.''
Bray, a junior, ranks fifth nationally with a passing efficiency rating of 194.77.
Florida quarterback Jeff Driskel is 34th at 154.64.
"Their quarterback play has been inconsistent,''
Fulmer said. "I don't want to get into everything, but that hasn't been a consistent football team.''
Fulmer, who was coach the most recent time Tennessee beat Florida, in 2004, said there are areas the Vols need to improve.
"I do think we need to run the football better,'' Fulmer said. "We haven't played against two outstanding defenses — this is a test. We need a running back to step up and make someone miss.''
Fulmer, an offensive lineman during his playing career at UT (1969-71) and offensive line coach with the Vols (1980-92) prior to his promotion, is encouraged by UT's growth on defense.
"The defensive front seems to be playing better,'' he said, "and something that struggled last year, the secondary, is certainly playing better.''
Fulmer also praised receiver Cordarrelle Patterson.
"I don't know that we had one that was any better than what he has been in two ball games,'' Fulmer said.
"You've heard me say a lot of times during the course of the years, it gets back to fundamentals,'' Fulmer said. "There are 11 guys out there on both sides of the ball trying to do the right things, and it's who makes the fewest mistakes.''
Mike Griffith covers Tennessee athletics. Follow him on twitter at http://twitter.com/MikeGriffith32