This study assesses the effective climate sensitivity (EffCS) and transient climate response (TCR) derived from global energy budget constraints within historical simulations of 8 CMIP6 global climate models (GCMs). These calculations are enabled by use of the Radiative Forcing Model Intercomparison Project (RFMIP) simulations, which permit accurate quantification of the historical effective radiative forcing. We find that long-term historical energy budget constraints generally underestimate EffCS from CO2 quadrupling and TCR from CO2 ramping, both by 12%, owing to changes in radiative feedbacks and changes in ocean heat uptake efficiency. Atmospheric GCMs forced by observed warming patterns produce lower values of EffCS that are more in line with those inferred from observed historical energy budget constraints. Understanding the discrepancies between modeled and observed historical surface warming patterns remains critical for constraining EffCS and TCR from the historical record.