[VRWCmember]

Past climate can be estimated from forensic information (tree rings, pollen in soil layers, et cetera). So that's actually pretty solid.

Yes, but the claims about global warming and especially global warming vis a vis "greenhouse gasses" or carbon emissions would depend on the accuracy of those estimates. If those estimates regarding temperatures from centuries ago are off by 3 or 4 percent due to changes in other variables that weren't included in the models, then the claims about global warming become more dubious, and the extrapolations and trends predicting continued warming as a result of human activity are pure fantasy.

[cogitator]

If those estimates regarding temperatures from centuries ago are off by 3 or 4 percent due to changes in other variables that weren't included in the models,

You don't understand how the oxygen isotope paleothermometer works. O18 and O16 are differentially fractionated in the atmosphere into water vapor in a relationship that is temperature-determined. (Due to the fact that O18 weighs more than O16 -- standard chemical thermodynamics). The resultant precipitation -- which ends up in ice cores -- has an O18/O16 ratio. The ratio now, at this global temperature, serves as a basis for comparison to any other time period. The O18/O16 ratio is determined by temperature. So the temperature at any other time in the past is determined based on the fractionation relationship -- there are no other variables involved.

So, when you see a temperature curve for the past ice ages, it's really a plot of the O18/O16 ratio, also called "del" O18. Frequently, rather than absolute temperature, the "delta" temperature (difference from a set standard temperature) is displayed, as shown below.

Deuterium can also be used the same way.