Jon Hamm has been getting a lot of attention since his hit series, Mad Men, debuted two years ago.

He’s won a Golden Globe and been nominated for an Emmy twice, he’s hosted Saturday Night Live, and his now-iconic character, Don Draper, has launched a veritable cult devoted to the well-dressed, self-assured advertising executive. There’s even a website set up in tribute, What Would Don Draper Do?

“The character certainly has resonated in a much larger way than I think anybody really expected,” Hamm says modestly, taking a break between shooting scenes for the third season, which premieres Sunday.

The square-jawed, affable 38-year-old actor — who spent years toiling in anonymous bit parts on various TV shows before landing Mad Men — is still incredibly appreciative of what the series has done for him. “When something like this happens, this sort of ‘overnight success,’ you pop up on a lot more people’s radar. Your phone starts ringing a lot more,” he says.

One of those phone calls was from Lorne Michaels, asking Hamm to host SNL, an experience he says seems “almost like it never happened.”

“That show has so much history. I’ve watched that show since I was a little kid,” Hamm says. “It was like summer camp.”

But we all have to go back to work sometime. And a look around the sleek Sterling Cooper offices — hidden inside a soundstage in Downtown Los Angeles — clears up some of the confusion left by last season’s cliffhanger. Don Draper’s name is still on his office door, and the calendar on his desk says it’s 1963, meaning the series has jumped forward again.

Setting the new season in 1963 raises a lot of obvious questions about big historical events, but the actor is understandably cagey about what will factor into the show.

“The challenge of the show is to show the big events happening, but you don’t want to show them in the way we’ve all seen them happen,” Hamm says. “For some people, they didn’t hear about Kennedy’s assassination on that day.”

Whether that’s a clue or not as to upcoming story lines, Hamm won’t say. He’s more concerned with the development of his character, anyway. And after last season’s partial reconciliation with his wife after she kicked him out, it looks like we can expect to see Don Draper trying to behave himself. “He’s trying to be a better person, he’s trying to be a better husband, father and man,” Hamm explains. “And maybe he’s not cut out for that.”

Hamm says he relishes leading the series’ outstanding ensemble cast. “No one’s on set more than me, so a lot of people are taking their cues from the way I am on set,” Hamm explains. “And I love that. I’m glad that I’m the person that gets to set that tone, because who wants to go to work where your boss is a douche bag?”

• Mad Men season three premieres this Sunday. Check local listings.