This question was sparked by reading this article in The Guardian. It appears that sediments from the Siberian Lake El'gygytgyn are offering a rare glimpse into the past and a model of a possible future.
The lake was formed 3.6 million years ago by a meteor strike, and it appears that the sediment record is unbroken and that the atmospheric concentration of CO2 was similar to the 400ppm we have today and the temperature at the time was 8 degrees C warmer than today.
While climate sensitivity (estimated) seems to be in the range of between 2 and 4.5 degrees C, there are major possible feedbacks which can amplify the effects and also the effects of global warming are likely to be more rapid and severe at the poles. This find of the lake sediments suggests that we may be in for more than we have so far estimated.
One of the issues is the inertia of the system. Even if we stopped emitting CO2 now, the temperature would likely continue to rise for the next 50 years or so.
And with the (predicted) effects of the arctic becoming ice free in the summer in 2 years (when, for example, loss of arctic summer sea ice has been linked to the recent harsh winters, flooding and droughts) and the possibility of the permafrost going at a 1.5 degrees C rise then we really can not be complacent.