Few statisticians can have inspired more passion than Bjørn Lomborg, the Danish academic who became famous as the author of the controversial (some would say contrarian) Skeptical Environmentalist, which set him up as perhaps the world's best-known critic of the dominant scientific view of global warming and the ensuing climate change.

Lomborg's prolific output has been almost matched by books rubbishing his work: critics have described him as selective, unprofessional and confused. Rajendra Pachauri, chairman of the UN's climate change panel, has compared him to Adolf Hitler – for the statistical crime of treating human beings too much like numbers.

Meanwhile, Time Magazine declared Lomborg one of the 100 most influential people in the world in 2004. The respected Cambridge University Press (CUP) has published many of his books in the UK and the US, and the award-winning documentary maker Ondi Timoner and X-Men films producer, Ralph Winter, are about to release a film of his 2007 book Cool It (which carries the subtitle: the first optimistic film about global warming).

The Danish Committee on Scientific Dishonesty once declared Lomborg guilty of exactly that, but a government review later cleared him.

Lomborg's latest book, published by CUP next month, is likely to reignite these passions, because it appears to contradict so much of what he has said before and because he is straying into newly controversial territory. He is advocating that much more attention and money be lavished on climate engineering methods, such as whitening clouds so that they reflect back more of the sun's heat.

Heat is something he is resigned to. When he gives talks, he says, he often meets "people who come up and say: 'I thought I'd hate you.'"

But Lomborg's record on climate change is more nuanced than the stereotype suggests. From the beginning, he has said global warming is happening and is largely caused by humans. However, he has been consistently critical of what he sees as exaggeration of how much this matters, and of policies to tackle the problem. These would achieve too little and cost too much, he argues, meaning the money would be better spent on, say, reducing malaria and HIV/Aids, or extending clean water and sanitation.

In an example of the approach that enraged Pachauri, Lomborg argues in Cool It that predicted temperature rises could save more than 1.3 million lives a year. This, he says, is because many more people would be spared early cold-related deaths than would be at risk from heat-related respiratory fatalities. (Other academics reject his figures.) Lomborg concludes that because of imbalances in where deaths occur, the proposed extension of the Kyoto protocol to cut carbon emissions would "save 4,000 people annually in the developing world [but] end up sacrificing more than a trillion dollars and 80,000 people annually."

Given this background, the title of Lomborg's new book immediately indicates a change of emphasis. It is called Smart Solutions to Climate Change: Comparing Costs and Benefits. This impression is reinforced by comments in the introduction that climate change is "undoubtedly one of the chief concerns facing the world" and "a challenge that humanity must confront".

Later in the book, reflecting on analysis by five economists of eight types of solution, he estimates that spending $100bn (£65bn) a year "could essentially resolve the climate change problem by the end of this century".

He finishes: "If we care about the environment and about leaving this planet and its inhabitants with the best possible future, we actually have only one option: we all need to start seriously focusing, right now, on the most effective ways to fix global warming."

Speaking to the Guardian about climate engineering as a back-up plan, he raises the possibility of "something really bad lurking around the corner": the small-chance, big-consequence outcome his previous work appeared to dismiss.

Not unexpectedly, however, Lomborg denies performing a U-turn. He reiterates that he has never denied anthropogenic global warming, and insists that he long ago accepted the cost of damage would be between 2% and 3% of world wealth by the end of this century. This estimate is the same, he says, as that quoted by Lord Stern, whose report for the British government argued that the world should spend 1-2% of gross domestic product on tackling climate change to avoid future damage.

The Stern report estimated that damage at 5-20% of GDP, however, not 2-3%. The difference, according to Lomborg, is that the two use a different "discount factor". This is the method by which economists recalculate the value today of money spent or saved in the future – or, to put it another way, the value today of this generation's grandchildren's lives. Neither is measurably "right", he says: they are judgments, albeit ones with a profound impact on subsequent analysis of the costs and benefits of spending money now to stop climate change.

Lomborg says false views of his position are held mostly by people who have never read his work. He says: "I keep trying to fight this, mainly because people often hear what I say through others." These intermediaries are often hostile critics, he adds.

Another cause of misunderstandings could be the difference between the content and the tone of his work. In it, brief statements about the unarguable fact of man-made global warming are accompanied by long arguments about how greenhouse gas emissions, the main man-made cause, and temperatures have been higher in the (very distant) past, and by claims that impacts such as rising sea levels and the threat to polar bears have been distorted.

Meanwhile, some statements appear to contradict each other directly. In the space of four pages of Cool It, he writes that "climate change will not cause massive disruptions or huge death tolls", that "the general and long-term impact will be predominantly negative", and that it is "obvious that there are many other and more pressing issues".

"The point I've always been making," he explains now, "is, it's not the end of the world. That is why we should be measuring up to what everybody else says, which is we should be spending our money well."

This detailed analysis by economists of how best to spend money to help the world's people was first reported in his book Global Crises, Global Solutions in 2004. It has now been institutionalised in the Copenhagen Consensus Centre, of which Lomborg is the director, and is the model for the latest book on climate "solutions".

This result is where Lomborg is most vulnerable to allegations of a volte-face on the need to take action on climate change and the value of doing so. But he says circumstances have changed. The first Copenhagen Consensus considered only the predominant idea of cutting carbon emissions through a cap or tax. When the exercise was repeated in 2008, however, the team examined new ideas. Lomborg says he then challenged himself and selected economists to look at eight different "solutions" (comprising 15 policy suggestions). These included boosting R&D in technology, cleaning up soot and methane, which also contribute significantly to global warming, planting more trees, and climate engineering. Critics may argue he should have carried out this study before rubbishing climate policies.

As a result, he is still deeply critical of the dominant, cutting-carbon approach, which four of the five economists who were asked to rank the options put at the bottom of their lists. Only Nancy Stokey, of the University of Chicago, ranked lower- and mid-level carbon taxes more highly, around the middle of her list. Instead, the book suggests the best policies would be investment in clean technology research and development, and more climate engineering development work. He suggests this could be funded by a $7-a-tonne tax on carbon emissions, which he says would raise $250bn a year. Of this, $100bn could be spent on clean-tech R&D, about $1bn on climate engineering, $50bn on adapting to changes (building sea defences, for example), and the remaining $99bn or so on "getting virtually everybody on the planet healthcare, basic education, clean drinking water, and so on. It seems a pretty good deal," he says.

Lomborg is not alone in finding fault with the Kyoto process, which many variously agree has been too slow to deliver, too vulnerable to unkept promises, and unrealistic in restraining the aspirations of developing countries. Critics add that it has proved to be a clumsy, ineffective way of delivering necessary investment in energy efficiency and clean electricity, and has resulted in often unnecessarily expensive policies. For most policy areas, such as crime, says Lomborg: "We say to people, what are the smartest ways to deal with this?" Curiously, with climate change, they say there's a right solution: that's cutting carbon."

The "biggest bang for the buck" Copenhagen Consensus approach is instinctively commonsense. But it is flawed, say critics, because it relies too heavily on the huge assumptions needed to convert human wellbeing and suffering into numbers (such as the discount rates) and excludes many factors that have simply never been quantified, such as the predicted total loss of coral reefs and other impacts of rapid ocean acidification.

Professor Katherine Richardson, a marine biology expert and vice-dean of science at the University of Copenhagen, says: "A lot hinges on whether you think that societal decision should be made by economists alone. [For example] I can think of much cheaper ways of taking care of our elderly in society than building expensive and modern nursing homes. In reality, we get very little return for that investment."

Many climate change scientists also fear huge disruption caused by changing tack will delay political action on avoiding the worst of the problem for a dangerously long time.

Lomborg's aggressively sceptical reputation will no doubt win few such people over, although he says he has no regrets about how he has conducted the debate. "Fundamentally," he says, "it would have been better if Pachauri or Stern were to make this argument. This isn't about ownership of the idea, but it's an idea we need to listen to if we want to get the climate fixed."

• Smart Solutions to Climate Change: Comparing Costs and Benefits is published by Cambridge University Press in September in the UK, October in the US