According to scientists, such a rise would be disastrous, condemning hundreds of millions of people to worsening drought, floods and storms.
A long list of world leaders, including many from nations most at risk from rising sea levels, have been pushing for delegates meeting in the Danish capital to limit the rise to between 1.5 and 2C.
But so far the summit has seen little more than two weeks of angry exchanges and procedural wrangling, with little progress towards a deal on the key issues.
On Friday Barack Obama, the US president, is due to arrive in Copenhagen hoping to give added impetus to the final negotiations.
The US was widely condemned for foot-dragging on climate change under former president George Bush, and Obama is hoping his presence at the summit's finale will demonstrate an about-turn in US policy.
|Protesters are angry that two weeks of talks have made little progress [AFP]
His arrival follows a pledge from Hillary Clinton, the US secretary of state, to contribute to a long-term fund worth $100bn a year by 2020 to help poor countries fund cleaner technology and shore up defences against worsening floods, drought, storms and rising seas.
However that pledge is contingent on an ambitious overall deal being completed at the talks.
Clinton also accused developing nations of backsliding on pledges to open their emissions control to scrutiny.
"There have been occasions in this past year when all the major economies have committed to transparency," Clinton told a press conference on Thursday.
"Now that we are trying to define what transparency means and how we would both implement it and observe it, there's a backing away from transparency - and that to us is something that undermines the whole effort that we're engaged in," she said.
Clinton said any deal that did not have sufficient transparency for all parties would be a "deal-breaker" for the US.
China and India, two of the world's biggest and fastest-growing carbon emitters, say they are willing to take voluntary measures to slow their growth of gas emissions.
|French President Nicolas Sarkozy said failure to reach a deal would be "catastrophic" [AFP]
But they are reluctant to accept tough international inspection and insist rich nations shoulder the main burden by accepting huge reduction targets.
"We should not continue to dwell on these issues that are dividing us. We should narrow our differences, otherwise we are facing a failure," Chinese Vice Foreign Minister He Yafei told reporters.
On Thursday Nicolas Sarkozy, the French president, warned the world faced a looming disaster if the summit failed to break the deadlock over carbon emissions.
"There is less than 24 hours. If we carry on like this, it will be a failure," Sarkozy said.
"Failure at Copenhagen would be catastrophic for all of us."
Obama will be joining more than 120 world leaders attending the final leaders summit on Friday.
"Now we rely on the willingness of all parties to take that extra step that would enable us to make the deal that is expected of us"
Lars Loekke Rasmussen, Danish PM and conference chairman
He is due to address the morning plenary session before holding a bilateral meeting with Wen Jiabao, the Chinese premier, who will also address the summit, laying out China's position on emissions cuts.
But in the run-up to Friday's final day, the tone of government briefings indicated that few delegations were optimistic that a last-minute significant breakthrough was possible.
"Coming back with an empty agreement would be far worse than coming back empty-handed," Robert Gibbs, the White House spokesman, told reporters before Obama left Washington.
Jose Manuel Barroso, the EU Commission chief, said he expected Obama to announce further US action to push things forward "because if they don't do it, others will find an excuse also not to move."
On Thursday Angela Merkel, the German chancellor, warned prospects for a deal were "not good" as she criticised emissions pledges made by industrial nations as insufficient.
However Ban Ki-moon, the UN secretary general, was more optimistic, looking to talk up the prospects of an agreement saying he had "not seen anything that indicates we cannot seal a deal."
"There are more than 130 leaders here. If they cannot seal a deal, who can?"
Lars Loekke Rasmussen, the Danish prime minister and conference chairman, said on Thursday the climate summit - widely-touted as the last chance for a global deal - was "at a critical juncture".
"Now we rely on the willingness of all parties to take that extra step that would enable us to make the deal that is expected of us," he said.
Late on Thursday night leaders from 28 countries representing key blocs on the debate began a last-ditch meeting, hoping to hammer out a draft text on curbing emissions and tackling the worst effects of climate change.
The emergency meeting came after the European Union called on all parties "to urgently go to the outer limits of their flexibility" so that the talks could advance.