We have revised the method for estimating the uncertainty in climate system properties from Forest et al. (2002). To apply a fully Bayesian approach, we first approximate the response of the MIT 2DLO climate model with a statistical model that provides a response surface in the uncertain parameter space. The three-dimensional parameter space is defined as climate sensitivity (S), rate of deep-ocean heat uptake (Kv), and the net aerosol forcing (F{aer}) and have been identified as the three major uncertain quantities that affect the ability to simulate accurately the 20th century climate record. The availability of this response surface permits one to perform a full Markov-Chain Monte-Carlo (MCMC) sampling of the joint posterior distribution of the parameters. This approach facilitates the testing of methodologies for performing the more computationally intensive project using the complete MIT 2DLO climate model, which is infeasible with current computer resources.