Coupled climate models exhibit a wide range of climate sensitivities. Further, their equilibrium and transient climate sensitivities are poorly correlated. That is, some models with relatively high equilibrium heat capacities have relatively low transient climate sensitivities. There are at least two possible causes for this: climate non-linearity, where certain feedbacks only "kick in" after some finite climate forcing is attained, and where this finite level of forcing varies from one model to another, or variations in effective heat capacity. In this study we use analysis of the covariance of surface temperature and surface energy fluxes in the IPCC AR4 model runs to diagnose effective heat storage in the various models, in order to partially explain the range of transient model climate sensitivity. Dramatic differences in both the global effective heat capacity and in the pattern of surface heat uptake are found among the models. We compare the model results to results from analysis of the ECMWF reanalysis data set, and discuss the reliability of the reanalyzed fluxes as a test of the model fluxes.