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. It is shown that the transient climate response to cumulative emissions of carbon (TCRE) is approximately proportional to the transient climate response (TCR), suggesting that observational constraints imposed on climate sensitivity in the model ensemble can reduce uncertainty in RCB estimates.