Modern climate system models make use of numerous tunable parameters. Uncertainty in these parameter input values should be propagated to model outputs. By matching model outputs with observed climate data (20th-century deep ocean, surface, and upper air temperatures), we perform coherent posterior inference over the model parameters. Our work extends the analysis of Forest et al. (2002) through the application of model interpolation, Markov chain Monte Carlo posterior simulation, and a posteriori model selection. Forest et al. (2002) identified three critical and uncertain input parameters for the MIT 2DLO climate model: climate sensitivity (CS), deep-ocean heat uptake (KV), and net aerosol forcing (FA). Their work sampled the climate model diagnostics on a nonuniform 3D grid. We interpolate the climate model diagnostics over the empty regions of this grid, providing an approximation of a continuous climate model response for use likelihood functions. The likelihood functions applied depend on valid estimation of covariance among the elements of the multivariate diagnostic.