Relative entropy, which is a measure of the difference between two probability distributions, has been calculated for the simulations of the climate of the 20th century from 13 climate models and the observed surface air temperature during the past 100 years. This quantity is used as a measure of model fidelity: a small value of relative entropy indicates that a given model's distribution is close to the observed. It is found that there is an inverse relationship between relative entropy and the sensitivity of the model to doubling of the concentration of CO2. The models that have lower values of relative entropy, hence have higher fidelity in simulating the present climate, produce higher values of global warming for a doubling of CO2. This suggests that the projected global warming due to increasing CO2 is likely to be closer to the highest projected estimates among the current generation of climate models.