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In the following, we test the validity of a one-box climate model as an emulator for atmosphere-ocean general circulation models (AOGCMs). The one-box climate model is currently employed in the integrated assessment models FUND, MIND, and PAGE, widely used in policy making. Our findings are twofold. Firstly, when directly prescribing AOGCMs' respective equilibrium climate sensitivities (ECSs) and transient climate responses (TCRs) to the one-box model, global mean temperature (GMT) projections are generically too high by 0.5K at peak temperature for peak-and-decline forcing scenarios, resulting in a maximum global warming of approximately 2 K. Accordingly, corresponding integrated assessment studies might tend to overestimate mitigation needs and costs. We semi-analytically explain this discrepancy as resulting from the information loss resulting from the reduction of complexity. Secondly, the one-box model offers a good emulator of these AOGCMs (accurate to within 0.1K for Representative Concentration Pathways, RCPs, namely RCP2.6, RCP4.5, and RCP6.0), provided the AOGCM's ECS and TCR values are universally mapped onto effective one-box counterparts and a certain time horizon (on the order of the time to peak radiative forcing) is not exceeded. Results that are based on the one-box model and have already been published are still just as informative as intended by their respective authors; however, they should be reinterpreted as being influenced by a larger climate response to forcing than intended.