As you may have noticed, it's been a bit on the balmy side this summer. What better time to lower temperatures with the coolest actress on the planet? It's Greta Gerwig. Crisply blonde, strong of feature, the Californian can been spotted in mainstream pictures such as throwaway comedy No Strings Attached and that ill-advised remake of Arthur. But her true metier is the classier end of American independent cinema.

In the middle of the past decade, Gerwig, now 29, became a leading figure in the cinematic non-movement that – thanks to the lowness of its key – came to be known as "mumblecore". That's her showing characteristic restraint in Mark and Jay Duplass's Baghead, Joe Swanberg's Hannah Takes the Stairs and Noah Baumbach's Greenberg. This week, she can be seen as the title character in Baumbach's endlessly delightful Frances Ha.

Hello, Ms Gerwig. Let us first point out how much we like your forename. There aren’t enough Gretas about any more.

“Yeah, I love the name too,” she says. “It’s an old-fashioned name. It’s usually people’s grandmothers and so forth, so, I like that about it.”

You will be pleased to hear that Greta is not at all like the slightly sleepy characters she played in those first few independent pictures. She is, in person, closer to the exuberant, positive Frances (though a deal more focused). It can’t be fun living with that “Meryl Streep of Mumblecore” reputation? The phrase keeps appearing in interviews. Mind you, what actor would object to being the Meryl Streep of anything?

“Hey, just being the Meryl Streep of your own neighbourhood would be pretty cool,” she says. “None of that bothers me. I actually don’t get asked about it that much anyway. I always felt that, starting out, I gave it everything I had. I think when I am annoyed by any question it indicates that I am insecure about something. That doesn’t worry me.”

Of course, those of us who skirt the outer rings of the cinematic system can easily overstate the penetration of such concepts. It seems unlikely that too many viewers of Arthur were pondering her appearance in Baghead (which really does involve a fellow with a bag on his head).

"I did get to move on to a world where nobody even knew those movies existed, so I didn't feel quite as encumbered by it. It was harder for directors like Mark Duplass and Joe Swanberg to escape. You can't make a movie every week if you're a director."

In recent years, Gerwig has been on top form as a domineering college student in Whit Stillman's Damsels in Distress and as an American emigré in Woody Allen's To Rome With Love. But Frances Ha looks to be the film that will properly cement her reputation.

Co-written by Gerwig and Baumbach (her current romantic partner), the film follows the careering adventures of a supposed dancer – who doesn't dance all that much – as she travels from apartment to apartment in bohemian New York City (and briefly heads off for a disastrous holiday in Paris). Among the joys of the film is its slightly equivocal attitude to its heroine and her friends. Frances is certainly a bit of a pretentious nitwit, but she's kind, funny and, ultimately, rather admirable.

“In some ways that came out of a process. It was not entirely conscious,” Gerwig says. “We worked on the script quite hard. But we never tried to dictate who she was. We wanted to tap into the rhythms of her voice. Why was she arrogant? Why was she frustrating? If we do our best to show all her true colours then we won’t need to be any clearer about how we see her.”

That makes sense. Frances Ha seems also to offer us a few clues as to Greta Gerwig's personality and background. Both character and actor were raised in Sacramento. Frances and Greta both attended colleges that form part of the prestigious "Seven Sister" grouping: Vassar and Bernard respectively.

Where do the connections begin and end? Frances emerges as a girl’s girl. The film kicks off when her very best friend moves out of their apartment. The severing of that friendship seems quite traumatic for Frances. Is it wrong to assume that progressing through a same-sex institution such as Bernard makes a woman more, well, womanly?

"It does maybe shape you into a girl's girl but it also makes you a bit more of an androgynous girl because the relationships in your life are primarily between you and other women," Gerwig says. "You don't get to play other roles. We purposefully gave her a name that can almost be a boy's name as well. She's a woman, but sexuality is not the main force. I guess going to an all-girl's school affected my development. In Frances, those things are pushed to the extreme."

Gerwig was raised in the Californian state capital as part of a firmly middle-class family. Her dad was a financial consultant and her mother was a nurse. She did develop an interest in acting at school and she thought of applying to drama college, but she ultimately ended up majoring in English and philosophy at Bernard. That college is situated in the Morningside Heights area of Manhattan and, after graduation, Greta lunged towards the city’s artistic underworld.

How did her parents take it? Were they worried?

“Yes! I think they really were worried,” she says. “We had a conversation. They said I should do a master’s and then I could teach if it didn’t work out. It was nerve-wracking. They wanted me to become an attorney or a doctor or something.”

So there weren’t any artists in the Gerwig clan? She’s the first to run away and join the troubadours?

“Well, nobody was doing it professionally,” she says. “I knew a lot of people who were doing it as dedicated amateurs. My dad played trumpet in a jazz band in Sacramento. But the arts were seen as a hobby, not a job. It was not until I got to New York that I met professional writers and artists. That was formative. I knew there were such people, but I never really imagined that was for me.”

While she was at Bernard, she took a few acting classes. One of her teachers spotted her talent as a writer and – to further muddle her ambitions – suggested she focus her attentions on a playwriting course. She has practised the two disciplines throughout her career. She has appeared in and co-written such pictures as Hannah Takes the Stairs, Nights and Weekends and Northern Comfort. So, right from the start, she was very much in control of her own artistic destiny.

“Acting did begin taking over,” she muses. “I was doing so many movies based on improvisational acting, so, both parts of my brain were being activated all the time. I felt I was most useful as an actor when I was creating my own material.”

In a surprisingly short period, Greta became the face of a certain class of free-thinking, young New York bohemia. (Come to think of it, even her performance in Arthur ploughed that furrow.)

If you want somebody to discuss Hart Crane at a party in Williamsburg then Gerwig is your only woman. Indeed, Greta so embodies that Gotham attitude one has to remind oneself she is not actually from the city. Frances Ha is – as much as Woody Allen's Manhattan – an uninhibited celebration of the place.

‘There is something about not being from New York that sets you free to really love it,” she says. “You are allowed to fetishise it. If you are from there you don’t have the same notion of living your dream. I would feel that way even if I were unemployed and broke in the city. I’d still be living my dream. When Frances dances down the street it’s a way of saying: I live in motherf***ing New York!”

Frances Ha re-established Baumbach's reputation – flagging a little since his The Squid and the Whale from 2005 – and confirmed Gerwig as, well, both hot and cool. She seems, however, like the least likely person to crash into celebrity mayhem. You wouldn't catch Lindsay Lohan making time to voice a dog for a hip animated TV series. Yet that's her as "Pony" in Adult Swim's funky China, Il.

“Who doesn’t like a talking dog?” she giggles. “Everybody’s got to do one of those, don’t they?” You’re not wrong, girl.