Current climate model projections are uncertain. This uncertainty is partly driven by the uncertainty in key model parameters such as climate sensitivity (CS), vertical ocean diffusivity (Kv), and strength of anthropogenic sulfate aerosol forcing. These parameters are commonly estimated using ensembles of model runs constrained by observations. Here we obtain a probability density function (pdf) of these parameters using the University of Victoria Earth System Climate Model (UVic ESCM) - an intermediate complexity model with a dynamic three-dimensional ocean. Specifically, we run an ensemble of UVic ESCM runs varying parameters that affectCS, ocean vertical diffusion, and the effects of anthropogenic sulfate aerosols. We use a statistical emulator that interpolates the UVic ESCM output to parameter settings where the model was not evaluated. We adopt a Bayesian approach to constrain the model output with instrumental surface temperature and ocean heat observations. Our approach accounts for the uncertainties in the properties of model-data residuals. We use a Markov chain Monte Carlo method to obtain a posterior pdf of these parameters. The mode of the climate sensitivity estimate is 2.8°C, with the corresponding 95% credible interval ranging from 1.8 to 4.9°C. These results are generally consistent with previous studies. TheCS pdf is sensitive to the assumptions about the priors, to the effects of anthropogenic sulfate aerosols, and to the background vertical ocean diffusivity. Our method can be used with more complex climate models.