With the news that Steve Jobs will take another medical leave of absence from the company he helped found more than 30 years ago, Apple will lose its most recognizable public face. But the man tasked with filling in for Jobs’s day-to-day duties should be a familiar face to most Apple watchers.

Chief operating officer Tim Cook takes up the reigns from Jobs during the CEO’s medical leave. It’s a familiar role for Cook, who joined Apple 13 years ago. This is his third time in the Jobs-void hot seat—he acted as interim CEO in 2004, when Jobs underwent treatment for pancreatic cancer, and again for the first half of 2009 when Jobs received a liver transplant.

Why does Apple keep turning to Cook? The answer is twofold: His resume, and his track record.

Wired once described Tim Cook as “[a] quiet, soft-spoken, low-key executive,” and “the yin to Jobs’s yang.” He’s 50-years-old, holds a degree in industrial engineering from Auburn University, and an MBA from Duke University.

Cook left Compaq in 1998 to join Apple as its senior vice president of operations, and steadily rose through the ranks until he was awarded his current title of chief operating officer in 2005. He’s credited with reinventing Apple’s approach to inventory supply chains, keeping in-demand products in stock, and managing the carefully-timed release of new ones. Prior to Compaq, he worked at IBM and Intelligent Electronics.

During Jobs’s six-month leave in 2009, Apple’s stock under Cook’s leadership rose 67 percent, according to CNN. In fact, Apple’s board of directors—in a move nominated by Steve Jobs himself—rewarded Cook with a $22 million bonus for his work in Jobs’s absence; that works out to about $3.6 million each month he filled in for his boss. (With those bonuses, Cook’s total compensation neared $60 million for 2010.)

While Cook’s work ethic and detail-oriented mind are frequently lauded, some analysts have questioned whether—despite his undergraduate design degree and years at Apple—he lacks the design chops that Jobs brings to the table. “Tim Cook’s the guy who makes the trains run on time,” said Roger Key of Endpoint Technology Associates in a 2009 interview with Macworldthe last time Apple turned to Cook. “He’s not the creative genius… Even though in some sense he is an excellent manager and is the backstop for Steve … that’s not going to do anything except make the trains run on time. That’s not going to decide what the train should look like in five years.”

CNN, however, quotes Gartner analyst Carolina Milanesi as saying, “There is a lot of respect for Tim Cook internally at Apple and externally, and he has proved to be able to drive the company well.”

Of course, as Macworld has explained in the past, Apple isn’t run by Steve Jobs corralling a team of lackeys. While Jobs’s contributions are obviously many, Cook gave this lengthy answer when asked about Jobs’s health on an earnings call in January 2009:

There is an extraordinary breadth and depth and tenure among the Apple executive team. And these executives lead over 35,000 employees that I would call all “wicked smart.” And that’s in all areas of the company, from engineering, to marketing, to operations, sales, and all the rest.

And the values of our company are extremely well-entrenched. You know, we believe we’re on the face of the Earth to make great products, and that’s not changing. We’re constantly focusing on innovating. We believe in the simple, not the complex. We believe that we need to own and control the primary technologies behind the products that we make, and participate only in markets where we can make a significant contribution. We believe in saying no to thousands of projects, so that we can really focus on the few that are truly important and meaningful to us. We believe in deep collaboration and cross-pollinization of our groups, which allows us to innovate in a way others cannot. And frankly, we don’t settle for anything less than excellence in every group in the company, and we have the self-honesty to admit where we’re wrong, and the courage to change.

And I think regardless of who is in what job, those values are so embedded in this company that Apple will do extremely well. And I would just reiterate a point Peter made in his opening comment, that I strongly believe that Apple is doing the best work in its history.

Cook's public profile as an Apple senior executive has continued to rise in recent years—likely by some combination of coincidence and design. Few top-level executives at Apple ever emerge from Jobs's shadow, but Cook has done so repeatedly in the past few year. It was Cook (along with senior vice president of Mac hardware Bob Mansfield) who joined Jobs on stage during the July press conference on iPhone 4 antenna issues, Cook who kicked off October’s Back to the Mac event, and Cook who delivered the news last week that the iPhone 4 would come to Verizon. Add these to Cook’s regular appearances on quarterly earnings calls with Wall Street analysts, and you get an executive who’s clearly playing an increasing role in Apple’s public relations efforts.

Cook’s drive for excellence at Apple is perhaps no better reflected than in this choice tidbit from a profile on him in Fortune headlined “The genius behind Steve.”

…[Cook] convened a meeting with his team, and the discussion turned to a particular problem in Asia. “This is really bad,” Cook told the group. “Someone should be in China driving this.” Thirty minutes into that meeting Cook looked at Sabih Khan, a key operations executive, and abruptly asked, without a trace of emotion, “Why are you still here?”

Khan, who remains one of Cook’s top lieutenants to this day, immediately stood up, drove to San Francisco International Airport, and, without a change of clothes, booked a flight to China with no return date, according to people familiar with the episode. The story is vintage Cook: demanding and unemotional.

Should Steve Jobs by choice or necessity ever need a full-time replacement at Apple, it will of course be the board’s decision to decide who should fill his black turtleneck. But with Tim Cook taking over now for the third time in seven years—and his consistent track record when called upon thus far—one might expect that Apple’s future is already in safe hands.

Disclaimer: The writer owns a small number of shares in Apple.