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The transient climate response (TCR) quantifies the warming expected during a transient doubling of greenhouse gas concentrations in the atmosphere. Many previous studies quantifying the observed historic response to greenhouse gases, and with it the TCR, use multimodel mean fingerprints and found reasonably constrained values, which contributed to the IPCC estimated (>66%) range from 1 degrees to 2.5 degrees C. Here, it is shown that while the multimodel mean fingerprint is statistically more powerful than any individual model's fingerprint, it does lead to overconfident results when applied to synthetic data, if model uncertainty is neglected. Here, a Bayesian method is used that estimates TCR, accounting for climate model and observational uncertainty with indices of global temperature that aim at constraining the aerosol contribution to the historical record better. Model uncertainty in the aerosol response was found to be large. Nevertheless, an overall TCR estimate of 0.4 degrees-3.1 degrees C (>90%) was calculated from the historical record, which reduces to 1.0 degrees-2.6 degrees C when using prior information that rules out negative TCR values and model misestimates of more than a factor of 3, and to 1.2 degrees-2.4 degrees C when using the multimodel mean fingerprints with a variance correction. Modeled temperature, like in the observations, is calculated as a blend of sea surface and air temperatures.