And quickly. In a couple of hours the dapper Don of Mad Men fame will be working the red carpet in London for a new Disney movie, Million Dollar Arm. For now, however, deep in interview mode, he looks more like Grizzly Adams, with desert island beard and hair to match.
Changing from whiskery to clean shaven can be done within the hour with the help of a good barber, but going from Don to Disney? That is quite the transformation, but if anyone can sell the pitch, Hamm can.
Million Dollar Arm, directed by Craig Gillespie, is based on the true story of a struggling sports agent, JB Bernstein, played by Hamm, who travels from LA to India in search of a cricketer he can turn into a major league baseball player. Hamm once had his own dreams of becoming a pro baseball or football player.
"I rapidly realised that my talents did not necessarily lie in that arena," says the 43-year-old when we meet in London. "So, you do the next best thing, you become an actor and you can fake it."
Among the sports he plays today is tennis. He was at the US Open in New York in 2012 when Andy Murray won his first Grand Slam. "It was so thrilling to watch him win it. Especially after coming so close so many times, to actually break through. To see those guys win their first major is so great."
The first half of Million Dollar Arm was shot in India in the spring. It is a season Bollywood knows to avoid because the temperatures can hit three figures before noon. The heat remains one of a jumble of toasty memories for Hamm.
"Everything was new. India is such an amazingly rich tapestry, not only from a cultural standpoint but from a religious and culinary standpoint. It would send me to Wikipedia every day when I got home. I'd want to learn more about whatever I had seen or heard that day."
On set there was no need to fake sweat on the actors. It was all real. Quite the change from Mad Men, the Emmy-winning television show so cool it should have come with frostbite warnings. When Hamm read the pilot script he thought it was the best he had ever seen. "It just hooked me immediately. I thought if the rest of the show can be as good as this one script then we might have something here."
By the time the show about Madison Avenue advertising executives started filming in 2007, the Missouri-born Hamm was 36. He had followed the usual script for an actor: moving to LA, becoming a waiter, and going for audition after audition. The change to his life, when it happened, was swift and extraordinary. It was something he thought about recently while filming the television show A Young Doctor's Notebook with Daniel Radcliffe.
Hamm has nothing but admiration for the way the Harry Potter star has handled fame. "He is a perfect example of how to do it. A big reason is he's got very, very good parents, but he also surrounds himself with really good people. It's a very strange experience to go through. You very much feel like you are looking at yourself from a mile high."
Hamm's mother died when he was 10, and his dad a decade later. The support of friends, their parents, and his teachers got him through. He is particularly grateful for the help he received from his high school, so much so that he went back there to teach drama for a year, and he has endowed a scholarship in his mother's name.
"Without it [the high school] I don't know how I would have done. I learned a lot there and met a lot of incredibly inspiring people. It gave me basically a new lease on life after experiencing loss at such a young age."
Now that the final series of Mad Men has finished filming - it will air next year - there has been a breakout of the Mad Men (and women) from the small screen to the big. John Slattery (Roger) has directed his first movie, God's Pocket, starring Christina Hendricks (Joan), while Elisabeth Moss (Peggy) is filming High Rise, an adaptation of the JG Ballard novel.
In an outstanding cast of characters, the philandering, mysterious, hard-drinking Don was the standout. Was Hamm amazed that men wanted to be this character and women wanted to date him?
"I don't know why anybody would want to date that guy," he laughs. "He's a pretty bad dude to date." Not a keeper, then? "Not so much."
With so many sides to him, however, Don was the kind of gift to an actor that kept on giving. That said, it was time to move on.
"The last thing I want to do is keep banging on that one piano key and playing the same person over and over because it's boring, not only as an actor but it's boring as an audience member. I got an incredible opportunity with Don to play a character that has a lot of shades. He's funny at times, dark at times, brooding, romantic, sad, loving, all of those things."
Hamm combined his time on the show with parts in movies including Friends with Kids (directed by his long-time partner, the writer and actor Jennifer Westfeldt), Bridesmaids, and Ben Affleck's The Town. He has shone in television comedies including 30 Rock, sending up his own good looks by playing the "so handsome, so, so stupid" boyfriend of Liz Lemon. All of this means that if more lead roles come his way, in comedy or drama, he is ready.
Before we leave Mad Men, time to clear up one thing. To date, Hamm is best known for playing Don Draper, an unreconstructed product of his Sixties times, and, in Bridesmaids, Ted, the sexist, selfish and deep as a puddle boyfriend of Kristen Wiig's Annie. So, is Hamm really a hard core feminist at heart? He laughs.
"I don't know if I'm a hard core feminist [but] I was raised by a single mom for the majority of my growing up. I tend to be attracted to very strong women, I think Jenn is a good example of that. Very intelligent, talented, charismatic women. There's a reason Annie doesn't end up with Ted at the end of the day. He's not the greatest guy for her."
After Million Dollar Arm, Hamm's next film is the animated blockbuster Minions, in which he plays Sandra Bullock's husband. As a comic book fan from childhood, he has not ruled out one day joining the ranks of superheroes.
"If the right character was to bounce or fly or jet into my life that would be pretty cool. But we're kind of running out of them aren't we, it seems like all the good ones are taken." He did, however, draw inspiration from a British sport he found on the TV the other night while channel surfing: Darts.
Don Draper as Dart Man? "There you go. The power of the pint, the belly and the elbow. From the oche to the cineplex."
Million Dollar Arm is in cinemas now.