Though initially skeptical, investors now seem to trust Green’s vision for the 171-year-old company. The stock, which hit an abysmal £0.14 last summer, dipped even lower upon her announcement as CEO of the company (she has no experience in travel). Since then, she’s won over shareholders by focusing on key decisions like firing and hiring, bringing in McKinsey as a management consultant, driving Thomas Cook’s new strategy to trigger profitable growth, and launching that strategy to the capital markets to refinance the business (it raised £1.6 billion in May). Green’s now been at the company for 336 days, and the stock’s up to over £1.2.

“I had tens and tens and tens of calls from other CEOs, from the press, saying, ‘What are you doing? Why would you do this?’” Green recalls, citing the obvious risk in joining Thomas Cook. But the company intrigued her – its solid gross margins, scale, and brand – and she reached out to the chairman directly. “It was a really good business with a terrible balance sheet.” She knew nothing about travel, but convinced Frank Meysman that her transformation expertise as CEO of electrical component distributor Premier Farnell, where she grew its virtually nonexistent web business from 12% to over 55%, primed her for Thomas Cook’s top job.

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This isn’t the first time Green’s willingly jumped into an uncomfortable position. She spent the bulk of her career at Arrow Electronics (ARW), which acquired over 70 companies between the early-eighties and the mid-nineties. She often took on the jobs that didn’t interest the golden bulls – “the group of very talented guys who want to do the conventional thing,” she says – and then-CEO Stephen Kaufman pushed her to stretch herself. “I tend to pick the people or the situation that I want to work for, rather than, ‘Is this going to be good for my career?’” Green explains. While at Arrow, she brought together over 20 acquisitions across Europe, moved to sub-Saharan Africa to merge four companies as part of a complex joint venture, and lived in China as the sales director of the company’s Asia Pacific business (though she doesn’t speak Mandarin, Green eventually became president of the whole division).

Green’s attraction to risk is fueled by loss. She says she’s more comfortable with unpredictability than most and claims her fearlessness stems from her father’s death; he was diagnosed with a brain tumor when she was 11 and he passed away when she was 14. “When you’re a child and your family’s quite dominated by cancer, the worst that could happen has kind of happened,” she says, adding that grief counseling taught her to always focus on the positive. “What’s the worst that could happen [in my career]? I fail. But is that lymphoma or leukemia? No.”

And fail she has. The former history student says that her mistakes have shaped her current strategies. Green documents her entire career (her to-do lists are always electronic, but she pens her thoughts and experiences in Molskine books) and often refers to her extensive collection. She’s confident in her vision for Thomas Cook because of those books and the many case studies they contain. Green’s obsession with technology – she recently approved a joint venture with travel discovery platform Triporati – springs from a missed opportunity while she was senior vice president of Arrow’s Northern Europe business. The changing market slowed her pace: she backed the wrong process control environment and ethernet solution, wasting a considerable amount of time. “Don’t be unambitious. Don’t miss technology changes in that environment.”

Green also struggled while bringing together those four sub-Saharan African companies. She decided to move them to a new singular location, and also launch a new computer system and branded name all on the same day. Employee stress shadowed any sort of focused momentum. “I think sometimes when you’re a transforming CEO, you think everyone can work with the same pace and energy and stress,” she explains. At Thomas Cook, she understands the limits of the organizations’ abilities and has treated them with a gentler hand. “You have to record [your failures] and go back and think about them.”

Green thinks of Thomas Cook as her patient: she’s worked on the psychology – how are employees, bankers, customers feeling – then moved to the physiology – the company’s nerve endings, blood flows, and systems processes. Only after those areas improve can you look at the anatomy – the organizational structure – Green says. And even still, Green worries Thomas Cook could revert to its old way. “There is a staggering statistic about the number of people in remission from cancer who go back to their old way of eating and behaving,” she says. “If we get complacent, we’ll never get to what I think this company can do.”

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After the May night Thomas Cook raised new capital, the employees went to the pub to celebrate; Green returned to her desk and crafted a note of all the additional things the company needed to do. “What is so exciting about the next 20 and 40 and 60 days is no one can relax,” she declares. “I don’t have a thread of complacency in my soul.”

Now focused on delivering all the promises that hooked the bankers who bought into Thomas Cook’s refinancing round, Green’s prepared to do whatever it takes. “When you’re doing a turnaround, you have to believe you can sleep when you’re dead.”