The IPCC’s scientific assessment of the timing of net-zero emissions and 2030 emission reduction targets consistent with limiting warming to 1.5C or 2C rests on large scenario databases. Updates to this assessment, such as between the IPCC’s Special Report on Global Warming of 1.5C (SR1.5) of warming and the Sixth Assessment Report (AR6), are the result of intertwined, sometimes opaque, factors. Here we isolate one factor: the Earth System Model emulators used to estimate the global warming implications of scenarios. We show that warming projections using AR6-calibrated emulators are consistent, to within around 0.1C, with projections made by the emulators used in SR1.5. The consistency is due to two almost compensating changes: the increase in assessed historical warming between the IPCC’s Fifth Assessment Report (AR5) and AR6, and a reduction in projected warming due to improved agreement between the emulators’ response to emissions and the underlying assessment.