A remaining carbon budget (RCB) estimates how much CO₂ we can emit and still reach a specific temperature target. The RCB concept is attractive since it easily communicates to the public and policymakers, but RCBs are also subject to uncertainties. The expected warming levels for a given carbon budget has a wide uncertainty range, which increases with less ambitious targets, i.e., with higher CO₂ emissions and temperatures. Leading causes of RCB uncertainty are the future non-CO₂ emissions, Earth system feedbacks, and the spread in the climate sensitivity among climate models. The latter is investigated in this paper, using a simple carbon cycle model and emulators of the temperature responses of the Earth System Models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) ensemble. Driving 41 CMIP6 emulators with 127 different emission scenarios for the 21st century, we find almost perfect linear relationship between maximum global surface air temperature and cumulative carbon emissions, allowing unambiguous estimates of RCB for each CMIP6 model. The range of these estimates over the model ensemble is a measure of the uncertainty in the RCB arising from the range in climate sensitivity over this ensemble, and it is suggested that observational constraints imposed on the transient climate response in the model ensemble can reduce uncertainty in RCB estimates.