Climate models predict that if CO2 emissions ceased today, the current temperature anomaly of ~ 1° C would likely persist for thousands of years. Extending a widely-used energy balance model of Earth’s climate to the case of emissions cessation reveals how this post-emissions response is governed by the equilibrium climate sensitivity, transient climate response, and CO2 airborne fraction. Temperature invariance after emissions cessation is found to be particular to the historical rate of emissions, and is therefore not a fundamental property of climate.