We present a method for constraining key properties of the climate system that are important for climate prediction (climate sensitivity and rate of heat penetration into the deep ocean) by comparing a model's response to known forcings over the 20th century against climate observations for that period. We use the MIT 2D climate model in conjunction with results from the Hadley Centre's coupled atmosphere-ocean general circulation model (AOGCM) to determine these constraints. The MIT 2D model is a zonally-averaged version of a 3D GCM which can accurately reproduce the global-mean transient response of coupled AOGCMs through appropriate choices of the climate sensitivity and the effective rate of diffusion of heat into the deep ocean. Vertical patterns of zonal mean temperature change through the troposphere and lower stratosphere also compare favorably with those generated by 3-D GCMs. We compare the height-latitude pattern of temperature changes as simulated by the MIT 2D model with observed changes, using optimal fingerprint detection statistics. Interpreted in terms of a linear regression model as in Allen & Tett (1998), this approach yields an objective measure of model-observation goodness-of-fit (via the normalized residual sum of squares). The MIT model permits one to systematically vary the model's climate sensitivity (by varying the strength of the cloud feedback) and rate of mixing of heat into the deep ocean and determine how the goodness-of-fit with observations depends on these factors. This approach provides an efficient framework for interpreting detection and attribution results in physical terms. For the aerosol forcing set in the middle of the IPCC range, two sets of model parameters are rejected as being implausible when the model response is compared with observations. The first set corresponds to high climate sensitivity and low heat uptake by the deep ocean. The second set corresponds to low sensitivities for all values of heat uptake. These results demonstrate that fingerprint patterns must be carefully chosen, if their detection is to reduce the uncertainty of physically important model parameters which affect projections of climate change.