White ice reflects more sunlight than open water, acting like a parasol.
Melting of white Arctic ice, currently at its lowest level in recent history, is causing more absorption.
Prof Wadhams calculates this absorption of the sun's rays is having an effect "the equivalent of about 20 years of additional CO2 being added by man".
The Cambridge University expert says that the Arctic ice cap is "heading for oblivion".
In 1980, the Arctic ice in summer made up some 2% of the Earth's surface. But since then the ice has roughly halved in area.
"Thirty years ago there was typically about eight million square kilometres of ice left in the Arctic in the summer, and by 2007 that had halved, it had gone down to about four million, and this year it has gone down below that," Prof Wadhams said.
And the volume of ice has dropped, with the ice getting thinner:
"The volume of ice in the summer is only a quarter of what it was 30 years ago and that's really the prelude to this final collapse," Prof Wadhams said.
Parts of the Arctic Ocean are now as warm in summer as the North Sea is in winter, Prof Wadhams said.
Radiation absorbed
The polar ice cap acts as a giant parasol, reflecting sunlight back into the atmosphere in what is known as the albedo effect.
But white ice and snow reflect far more of the sun's energy than the open water that is replacing it as the ice melts.
Instead of being reflected away from the Earth, this energy is absorbed, and contributes to warming:
"Over that 1% of the Earth's surface you are replacing a bright surface which reflects nearly all of the radiation falling on it with a dark surface which absorbs nearly all.
"The difference, the extra radiation that's absorbed is, from our calculations, the equivalent of about 20 years of additional CO2 being added by man," Prof Wadhams said.
If his calculations are correct then that means that over recent decades the melting of the Arctic ice cap has put as much heat into the system as all the CO2 we have generated in that time.
And if the ice continues to decline at the current rate it could play an even bigger role than greenhouse gases.
UK weather effect
Professor Wadhams stresses that there are uncertainties - cloud cover over the Arctic could change and help reflect back some of the sun's radiation.
But then another greenhouse gas - methane, currently trapped in the Arctic permafrost - could be released with warming and make matters worse.
The melting ice could have knock-on effects in the UK. Adam Scaife, from the Met Office Hadley Centre told Newsnight it could help explain this year's miserable wet summer, by altering the course of the jet stream.
"Some studies suggest that there is increased risk of wet, low pressure summers over the UK as the ice melts."
There may be an effect for our winters too: "Winter weather could become more easterly cold and snowy as the ice declines," Mr Scaife said.
Opinions vary on the date of the demise of summer sea ice. The Met Office says it is not expecting the Arctic to be completely ice-free in summer until after 2030.
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