The results from 16 coupled atmosphere/ocean general circulation model (AOGCM) simulations are used to reduce internally generated noise and to obtain an improved estimate of the underlying response of 20th century global mean temperature to volcanic forcing. An upwelling diffusion energy balance model (UD EBM) with the same forcing and the same climate sensitivity as the AOGCM is then used to emulate the AOGCM results. The UD EBM and AOGCM results are in very close agreement, justifying the use of the UD EBM to determine the volcanic response for different climate sensitivities. The maximum cooling for any given eruption is shown to depend approximately on the climate sensitivity raised to power 0.37. After the maximum cooling for low-latitude eruptions the temperature relaxes back toward the initial state with an e-folding time of 29--43 months for sensitivities of 1--4¿C equilibrium warming for CO2 doubling. Comparisons of observed and modeled coolings after the eruptions of Agung, El Chich¿n, and Pinatubo give implied climate sensitivities that are consistent with the Intergovernmental Panel on Climate Change (IPCC) range of 1.5--4.5¿C. The cooling associated with Pinatubo appears to require a sensitivity above the IPCC lower bound of 1.5¿C, and none of the observed eruption responses rules out a sensitivity above 4.5¿C.