There are in fact two climate sensitivities- fast and slow.
The slow feedback accounts for future large sources of increased sensitivity, like feedback emissions from permafrost thaw and loss of ice
Fast (onset) and slow (onset) feedback sensitivity.
The fast onset feedbacks are the ones that immediately act in response to an increase in atmospheric greenhouse gases (GHGs). They are mainly atmospheric feedbacks in the air, like water vapor, clouds and minute suspended particles (aerosols). Some albedo cooling effect of snow and ice is included.
Water vapor is actually the main GHG because it is so abundant but its global warming effect is mainly a feedback response. Warm air holds more water vapor and that about doubles the warming caused just by a GHG increase.
Slow onset feedbacks are planetary responses to global warming like melting ice sheets and thawing permafrost. Warming wetland peat is a slow feedbacks and melting sub seafloor methane hydrate is considered a very slow feedback.
The fast feedback CS is taken to be 3°C by the scientists and the slow feedback sensitivity is not used in the assessments- a huge error in underestimating the actual warming that will occur over the long term future.
It was James Hansen who pointed out in a 2008 paper that the true climate sensitivity for the very long term is (6C), which is double the immediate fast feedback sensitivity (3C) that has been applied by the science since the first IPCC assessment in 1990.
It is the 'true' CS because it is protective of all future generations and life. The fast CS that does not include the large slow feedbacks is not protective. The slow FS is therefore by far the most policy relevant.
Slow feedbacks take a long time (hence 'slow') in response to global warming, but they greatly increase over time and are irreversible. They include loss of albedo cooling from ice melting and Arctic carbon feedbacks from warming wetlands and thawing permafrost, that release methane and carbon dioxide
The metric is fixed to allow for climate change modeling. However in the real world the climate sensitivity is dynamic - with warming it increases as does the risk of abrupt warming.
Range of uncertainty
Finally, there are wide ranges of uncertainty for all aspects of climate change modeling (IPCC 2007), and there is a wide range of uncertainty for the fast climate sensitivity that determines the entire assessment of climate chang
"... climate sensitivity only considers the surface mean temperature and gives no indication of the occurrence of abrupt changes or extreme events. Despite its limitations, however, the climate sensitivity remains a useful concept.. IPCC AR4 2007 8.6.2.1 Definition of Climate Sensitivity"
The fact is climate sensitivity is not a linear constant factor (as is the case in the science), it is dynamic increasing with time and temperature of warming. This is because of the many positive (bad) feedbacks that increase with warming and decline of carbon sinks due to climate change effects.