For decades, scientists have been seen as meek, dispassionate souls. But now, faced with widespread indifference to global warming, a small band of science radicals are getting angry. Will more follow suit?

James Hansen never expected to become a radical activist at the age of 65. He is a grandfather who loves nothing more than exploring nature with his grandchildren. He holds down a respectable job as the director of Nasa's Goddard Institute for Space Studies. But he is 70 now, and he has a police record.

Hansen gets himself arrested, testifies in court on behalf of others who have broken the law and issues public pronouncements that have made Nasa try to gag him – all because he can't bear the thought that his grandchildren might hold him responsible for a burned-out planet.

Hansen is the climate scientist's climate scientist. He has testified about the issue in front of Congress, but has had enough of the standard government response – "greenwash", he calls it. Last month, Hansen issued an uncompromising plea for Americans to involve themselves with civil unrest over climate change. "We want you to consider doing something hard – coming to Washington in the hottest and stickiest weeks of the summer and engaging in civil disobedience that will likely get you arrested," he says in a letter on grist.org.

However many Americans turn up to get arrested in Washington, it's unlikely that Hansen will end up sharing a cell with other scientists. He cuts a lone figure on the barricades; almost all scientists run shy of such public misbehaviour.

In private, science has always been a brutal, gladiatorial arena. To be successful you have to challenge established thinking, force out the old guard and prove beyond question that you are right. That takes extraordinary tenacity, resourcefulness and courage.

The tragedy is that these laudable attributes are rarely channelled into tackling areas where science highlights something of global concern. Yes, scientists compile and contribute to reports on issues such as climate change. But those reports are made public only when the scientists have agreed on the most conservative of conclusions, satisfying the lowest common denominator among those whose names appear on the documents.

The UN's climate monitor, the Intergovernmental Panel on Climate Change (IPCC), for example, issues reports that stand accused of underplaying sea level rises. According to a report published by the US National Academy of Sciences, levels may rise three times faster than IPCC estimates.

That is not to say that climate scientists don't privately agree about what is going on with our planet. In April 2010 a study published in the Proceedings of the National Academy of Sciences showed that nearly 98% of working climate scientists accept the evidence for human-induced climate change. The voices of dissent reported "for balance" come almost exclusively from researchers who are not publishing in the field.

Unfortunately, this consensus over climate change is in danger of becoming the world's best-kept secret. According to the World Bank's 2010 World Development Report, 17% of US citizens think that the properly scientific view is to be sceptical about climate change, while 43% believe that scientists are "evenly divided". Who is to blame for this gulf between reality and perception? The media? The government? No. When they are being honest, the scientists blame themselves.

And that's why Hansen – and a handful of other scientists – are bypassing traditional outlets for scientific results.

If Hansen gets arrested this summer, it will complete his hat-trick: he has already been arrested twice at environmental protests. In 2009 police dragged him and actor Daryl Hannah off a mountain road in West Virginia. They and hundreds of other protesters had sat down in protest at a local company's intention to access the mountain's coal deposits by packing it with explosives and blowing its top off. The second arrest came last year in Washington, at a protest over similar practices.

Hansen's attitude echoes that of Sherwood Rowland, who won a Nobel prize for his research into the effects of chlorofluorocarbon (CFC) gases on the ozone layer. "What's the use of having developed a science well enough to make predictions," Rowland said, "if all we're willing to do is stand around and wait for them to come true?"

Rowland's colleagues shunned him for his activism. Even the iconic environmentalist James Lovelock called for a "bit of British caution" in the face of what he saw as Rowland's "missionary" zeal for a ban on CFCs. In the end, it was only the terrifying discovery of a hole in the ozone layer over Antarctica that galvanised the politicians.

US academics Naomi Oreskes and Erik Conway have highlighted the disappointing timidity of scientists. On acid rain, climate change, tobacco marketing and the ozone crisis, they "would have liked to have told heroic stories of how scientists set the record straight" in their book Merchants of Doubt, but scientists fighting back have been "conspicuously scarce". "Clearly, scientists knew that many contrarian claims were false," they lament. "Why didn't they do more to refute them?"

The answer is, because of the party line established in the post-war era: offer advice only if asked.

Academic science is a relatively new profession: it sprang up after the second world war, when governments realised that whoever invested the most in science would win the next war. It quickly became a lucrative and safe career option. But there was a cost involved: science had to promise to behave itself.

The atomic bomb, the V2 rockets and the threat of nerve and mustard gases had all contributed to the view of science as something that had to be tightly controlled. "People hate scientists," biologist Jacob Bronowski observed in 1956. And so scientists developed an attitude of forelock-tugging subservience, "the monk of our age, timid, thwarted, anxious to be asked to help," as Bronowski put it.

While most scientists have learned keep their heads down, a few are beginning to argue that what a scientist knows must inform his or her personal opinions and values. That's why a group of young Australian climate scientists released an expletive-filled music video earlier this year. It was an angry rap aimed at those who question climate science while holding no qualifications in the field. They used the rather unscientific word "motherfucker" and poured scorn on "bitches" opposing a carbon tax.

Hearteningly, there may be more of this to come. Paul Nurse, the new president of the Royal Society, has said he would be happy to see scientists getting fully engaged with politics and involved with activism.

And scientists are no longer hated: they are, in fact, overwhelmingly popular, and much more trusted than politicians. A 2010 survey of European citizens revealed that 63% of people think government or academic scientists are best qualified to explain the impact of scientific and technological developments on society (only 11% think politicians should do the job). It's not just about explaining, either. A 2009 Pew survey revealed that three-quarters of the public would like to see scientists active in political debates about such issues as nuclear power or stem cell research.

Those who have hitherto fought within the ivory towers to establish the science of climate change now need to muster up enough courage to take their fighting spirit out of the laboratory and onto the streets. Activist scientists will soon find themselves wondering why they cowered in the shadows for all those years. After all, as Bronowski also said: "dissent is the native activity of the scientist".