Footage has been posted on the internet of a speech Lord Christopher Monckton gave to a conference in Los Angeles earlier this month.
In it he displayed a Nazi swastika next to a quote from Professor Garnaut.
Lord Monckton compared statements made by Adolf Hitler to Professor Garnaut's suggestion that people should accept the mainstream science of climate change.
"That again is a fascist point of view, that you merely accept authority without question. Heil Hitler, on we go," he said.
The Scottish peer is scheduled to speak at the Association of Mining and Exploration Companies (AMEC) conference in Perth next week.
Opposition Leader Tony Abbott, who met Lord Monckton last year, will also address the AMEC conference along with independent MP Rob Oakeshott and Liberal Senator Mathias Cormann.
Lord Monckton, a one-time adviser to former British prime minister Margaret Thatcher, is known around the world for his argument that humans are not damaging the climate.
Last year he told a Canberra audience that proponents of climate change wanted to establish a "world government... that would have shut down democracy worldwide".
On Tuesday night, Professor Garnaut criticised the Federal Opposition's climate policy stance, saying "bitterness and rancour" had arisen in the debate.
He dismissed the Coalition's stance to take direct action, saying carbon pricing "happens to be the low-cost way of meeting national targets".
"If countries want to shoot themselves in the foot by doing things in an expensive way they are free to do so. We would be foolish also to meet our targets in an expensive way," he said.
"There is no reason that carbon pricing should be a matter of partisan political division in Australia - and it wasn't only a few years ago."
He alluded to nations like Britain and New Zealand that have conservative governments and emissions trading schemes, saying action on climate change should transcend political boundaries.
"In much of the world, perhaps everywhere except in contemporary Australia and the United States, concern for global warming is a conservative as much as a social democratic issue," he said.
@'ABC'
The man is a complete fugn moron, bankrolled by Gina again no doubt...
