The challenge for delegates at the week-long meeting in Denmark's capital is to agree on ways of ensuring we do not exceed it - ever.
Why this year?
Two years ago in Bali, member nations of the UN Framework Convention on Climate Change (UNFCCC), which is convening the Copenhagen summit, agreed that they would accelerate their efforts and draft a long-term plan to avoid dangerous climate change. Their deadline for doing so is the close of this year's summit, on 19 December.
Hasn't the Kyoto protocol shown all this to be pointless?
Not necessarily. The Kyoto protocol was always intended as a first step. There are a number of differences this time around, most notably that the US opted out of the Kyoto protocol but is very much engaged in the Copenhagen process.
The objective of the UNFCCC is to prevent "dangerous" climate change. Although any amount of warming may have consequences - including biodiversity loss, changing weather patterns and disappearing coastlines - many climate scientists predict that some of those changes will be irreversible beyond 2 °C and others will pose a serious threat to millions of people. As a consequence, 2 °C has been adopted by politicians as the threshold for dangerous climate change.