But a year after Abbott's fall, Mathias Cormann – the very private West Australian senator known primarily as the guy with the Schwarzenegger accent – is now emerging as one of Turnbull's key lieutenants.

It was Cormann who last week shepherded the government's $6 billion omnibus savings bill through the Parliament, spearheading negotiations with Labor to achieve a rare bipartisan budgetary accord.

But it wasn't the first time.

Under Abbott and Turnbull both, the finance minister has been less The Terminator and more The Negotiator. He's done deals with Labor, the Greens and the crossbenchers to get bills through.

Most of them praise the way he does business.

"He is a class act," says crossbench king Nick Xenophon.

"He has an incredible work ethic. He is always on top of his brief. He really sets the benchmark. People have this image of him as the man with the Terminator voice but he's more than that. He is very much underrated – the quiet achiever of the government."

Cormann does do things quietly.

While he does plenty of media – and is a good performer, relentlessly on-message and rarely stuffing up – he usually sticks with the serious outlets like Sky News and the ABC. He wants to talk policy and isn't particularly interested in boosting his personal profile.

Indeed, he hates taking part in profile pieces. Asked to participate in one with Fairfax Media this weekend he politely declined: he may be the only politician on the planet who doesn't like talking about himself.

Liberal Democrats senator David Leyonhjelm says Cormann "is not the crossbench whisperer".

"But he is very, very focused," he says. "And he is quite a nice guy to deal with."

That's another common refrain.

Despite his serious and sometimes robotic public demeanour, Cormann is in reality really quite affable.

By all accounts, he seems to enjoy finding common ground, using goodwill and creative thinking to bridge ideological gaps.

Cormann has a good relationship with two of Labor's key players, shadow treasurer Chris Bowen and Senate leader Penny Wong. And it's notable that the last thing Labor's Stephen Conroy did before tabling his resignation speech last week was praise Cormann.

Labor insiders say Cormann is a straight-shooter and trustworthy – unlike some of his colleagues. One spoke of being "mystified" as to why George Brandis is still the government's Senate leader rather than Cormann.

When it comes to social policy like same-sex marriage, Cormann has more in common with the likes of Cory Bernardi and Eric Abetz than he does Turnbull. But unlike Bernardi and Abetz, Cormann has fully accepts that Turnbull's the boss, playing no part – discernibly at least – in the sniping or undermining.

If anything, he serves as a bridge between the mostly conservative Coalition senators and the prime minister's office.

"The PM really likes him and they're close now. They respect each other," says a source close to Turnbull. "He's indefatigable. He works his arse off and he's just really good at getting things done."

Xenophon says the Belgian-born 45-year-old – who only came to Australia in his 20s, shortly after learning English as his fourth language – is like a traditional post-war migrant: "They just work that little bit harder to give back to the country."

Cormann is more a classic Liberal "dry" than a modern social conservative. He cares about small government, budget discipline and the free market and isn't quite so concerned about what goes on in people's bedrooms. Budget repair is a big job: he doesn't have time to fight the culture wars.

"It would be good if we had a few more like him, to be honest," the Turnbull confidante says.