Current estimates of future climate change are quite uncertain - the IPCC TAR headline figure was 1.4 to 5.8 oC. But that doesn't mean quite what most people think it means, because it includes uncertainties in CO2 emissions, which themselves are large. So if you're interested in the uncertainties just from uncertainties in the models, or the change at 2*CO2, then you need a different number. This is then the climate sensitivity (equilibrium at 2*CO2) or more usefully (and somewhat smaller) what the IPCC call the Transient Climate Response or TCR, which is the temperature change at CO2 doubling following a 1% CO2 trajectory. The number would varies a bit, but not much, if you followed a different plausible trajectory. It is 1.1 to 3.1 oC IPCC, here. This needs to be said with the standard caveats: that the global figure conceals regional variations, and that the model range may or may not encompass the true range.
I mention this in particular because David King may have made this mistake over in his piece at Opendemocracy, saying: The most recent calculation, based on enormous computer programmes at a number of world centres, including the Hadley Centre for Climate Prediction and Research, yields global temperature increases of 1.5-6C for a doubling of carbon dioxide levels. So if by most recent he means IPCC, I think he has the wrong numbers. Unfortunately he doesn't source his statement, so he may well mean some more updated numbers.