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Abstract Simple climate models (SCMs) are computationally efficient and capable of emulating global mean output of more complex Earth system models (ESMs). In doing so, SCMs can play a critical role in climate research as stand‐ins for the computationally more expensive models, especially in studies involving low, spatial, and/or temporal resolution, providing more computationally efficient sources of climate data. Here we use Hector v2.5.0 to emulate the multiforcing historical and RCP scenario output for 31 concentration and seven emission‐driven ESMs. When calibrating Hector, sufficient calibration data must be used to constrain the model; otherwise, climate and/or carbon parameters affecting physical processes may be able to trade off with one another, allowing for solutions to use physically unreasonable fitted parameter values as well as limiting the application of the SCM as an emulator. We also present a novel methodology that uses the ESM range as a calibration data, which can be adopted when faced with missing variable output from a specific model.