"If I could come to work every day, do this stuff, then walk out of the rink and nobody knew who I was, I'd be the happiest guy in the world," he says. "That's just the way I am. It's my personality."
It's tough for him to be anonymous, however, when he's three wins from a second Stanley Cup championship in three years. Especially after he's taken his team to the playoffs in each of his six years as coach and has the second-most postseason victories of any NHL coach in that stretch.
He would get his 50th, one less than Mike Babcock of Detroit, with a win Monday night in Game 3 that would give the Bruins a 2-1 lead over the Chicago Blackhawks in the best-of-seven series.
Then there's the recognition Julien really doesn't want the repeated rumblings that he might get fired if he doesn't win a particular postseason series.
Julien was honored as coach of the year for his regular-season performance in 2008-09. But the next season when the Bruins lost to the Philadelphia Flyers in the best-of-seven Eastern Conference semifinals after winning the first three games, there were calls for his exit.
Good thing general manager Peter Chiarelli, a staunch supporter of Julien, didn't listen.
The next year the Bruins captured their first Stanley Cup since 1972, winning three of their four series in seven games and taking the title with a 4-0 victory in Vancouver in Game 7.
But when Boston lost to Washington in the first round last season, the critics returned. And it didn't get better when the Bruins nearly blew a 3-1 series lead to the Toronto Maple Leafs in the first round this year.
"I've been here for six years. I think I've been fired five times," Julien said to laughter. "You know, those kinds of things really are not important to me. What's important is the results. As long as the people I work for appreciate what we do, that's what matters. At the end of the day, winning hockey games for our fans and for the city is what matters to me. That stuff is really no bother to me."
He said that after the Bruins swept the favored Pittsburgh Penguins in the conference finals.
His detractors have been silenced.
"I think definitely, Claude takes a lot of heat, too, when things don't go well, but he handles it on an even keel," left wing Daniel Paille said. "I think it kind of relates the message to us as players and I think that's why we've been able to succeed so far, but we're not done."
The speedy Paille has reason to admire his coach.
He scored the winning goal in Boston's 2-1 overtime win in Game 2 in Chicago after Julien put Tyler Seguin, maybe even faster than Paille, on his line after the team's listless opening period Saturday night. Seguin made a perfect pass from the boards and Paille fired the puck past goalie Corey Crawford.
Sometimes knocked for playing too defensively and being slow to change, Julien made the right move to generate offense.
"I think he makes great adjustments," Seguin said. "You've got to give him credit. He's a great coach. He's definitely got a lot of experience at this level and in these situations."
He could have had more.
But with three games left in the 2006-07 regular season and the New Jersey Devils leading the Atlantic Division, Julien was fired by general manager Lou Lamoriello, who took over as interim coach. The Devils lost in the Eastern Conference semifinals
In his last game, Julien beat the Bruins 3-1. It was the Devils' fourth win in five games, but Lamoriello said he felt they weren't ready for the playoffs. Julien reacted calmly.
"You're thinking you're going to be heading into the playoffs and you're getting mentally prepared for that," he said then. "You don't want to be let go with three games left in the season, but at the same time, everybody has a job to do, and that's a part of the game you have to understand."
The Bruins hired him before the next season after one year under Dave Lewis and two straight finishes out of the playoffs. Since then, they're 275-146-56 in the regular season and 49-31 in the playoffs.
Julien carried them through a tough stretch this season when they lost 14 of 22 games and were outscored in the last three of those 17-5.
But he talked with his players, tweaked their strategy and led them to nine wins in their last 12 games entering the playoffs.
"I enjoy the job. I enjoy being around players. I enjoy the whole process of this work," Julien said, "just don't like the limelight that comes with it. I'm low profile. That's just the way I am."
And this time, the even-keel coach's team was definitely ready for the playoffs.
"It shows how our team is," goalie Tuukka Rask said. "We don't like to talk about ourselves too much on a high note and not try to push ourselves to the front page, but he's definitely done a tremendous job here and he deserves a lot of credit for that."