The major greenhouse gas is water vapour, and the nature of CO2 / water vapour interactions is not clearly understood. Moreover, James Hansen (2000) downplayed the role of CO2 as a greenhouse gas.
Antarctic ice cores in one study show carbon dioxide concentrations increased by 80 to 100 ppm about 600 years after the warming of the last three deglaciations, while in another study Antarctic ice core data show that CO2 levels lag an increase in temperature by 900 to 1200 years.
World Climate Report shows that annual growth in concentrations of CO2 in the atmosphere have remained essentially flat from 1975 to the present - during a time of maximum production of CO2 from fossil fuels. This casts doubt on the claim that rapid and dramatic build-ups of CO2 will occur in the future.
We know that CO2 from the burning of fossil fuels was not the cause of dramatic historical climate changes, for example, 1000 years ago, in the Medieval Warm Period or in the Little Ice Age that followed from about 1350 to about 1860. We are still emerging, in an oscillating fashion, on the warming trend that came after the Little Ice Age. Global historical temperature data is readily available, for example Canada, Mediterranean, Alaska, China and Canadian Rockies.
In the 20th century, there was little correlation between temperature changes and CO2 levels. Some surface temperature measurements show a 0.5°C rise over the past 100 years. However, that average hides some significant details. From 1905 to 1940, a rise of about 0.5°C was measured, during which time there was an imperceptible rise in CO2. From 1940 to 1975, the temperature decreased about 0.2°C, while CO2 levels started to increase more rapidly. The out-of-sync relationship is obvious.