We present probabilistic ranges of uncertain climate model properties obtained by comparing observational data with results produced by versions of the MIT 2D climate model with different values of climate sensitivity, rate of oceanic heat uptake, and strength of net aerosol forcing. Results presented by Forest et al. (2000) (GRL, {\bf 27}, 4, 569--572) did not include uncertainty in aerosol forcing and were based only on the data for upper air temperature changes from 1961 to 1995. In the present, study we include data from two additional independent data sets, namely surface air and deep ocean temperature changes. For surface data, we compare a spatio-temporal pattern of temperature change (decadal and zonal averages) for the 1946-1995 period using the average for 1906-1995 as the baseline climatology. We use a modified detection algorithm to estimate the goodness-of-fit between modeled temperature changes and the obervational record. Required estimates of climate natural variability were obtained from control runs of atmosphere-ocean general circulation models. In the case of the deep ocean temperature we compare trend in global average annual mean temperature averaged over the top 3000~m. The observational error and the natural variability are combined to provide a range of trends that are not inconsistent with the observed data. Goodness-of-fit statistics provide constraints on model properties when the model response to applied forcings becomes inconsistent with the observations. Using upper air temperatures, two regions of parameter space are rejected: a ``weak response'' region (low climate sensitivity for all ocean heat uptakes and aerosol forcings) and a ``strong response'' region (high climate sensitivity combined with weak ocean heat uptake and weak aerosol forcing). The deep ocean temperature changes provide a rejection of different regions of parameter space. A large temperature change in the deep ocean requires a high climate sensitivity, a large deep-ocean heat uptake, and a weak aerosol forcing. Provided the aerosol forcing is not too large, the high climate sensitivity and high heat uptake region is rejectable. Finally, the latitude-time structure of the surface temperature change provides strong constraints on the net aerosol forcing placing bounds at 0 and 1.5 W/m$^2$ of radiative cooling at the 5\% significance level. The uncertainty in the composition and timing of aerosol-like forcings remains.