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Recent research has demonstrated that global mean surface air warming is approximately proportional to cumulative CO₂ emissions. This proportional relationship has received considerable attention, as it allows one to calculate the cumulative CO₂ emissions ('carbon budget') compatible with temperature targets and is a useful measure for model inter-comparison. Here we use an Earth system model to explore whether this relationship persists during periods of net negative CO₂ emissions. Negative CO₂ emissions are required in the majority of emissions scenarios limiting global warming to 2 °C above pre-industrial, with emissions becoming net negative in the second half of this century in several scenarios. We find that for model simulations with a symmetric 1% per year increase and decrease in atmospheric CO₂, the temperature change (ΔT) versus cumulative CO₂ emissions (CE) relationship is nonlinear during periods of net negative emissions, owing to the lagged response of the deep ocean to previously increasing atmospheric CO₂. When corrected for this lagged response, or if the CO₂ decline is applied after the system has equilibrated with the previous CO₂ increase, the ΔT versus CE relationship is close to linear during periods of net negative CO₂ emissions. A proportionality constant—the transient climate response to cumulative carbon emissions (TCRE)− can therefore be calculated for both positive and net negative CO₂ emission periods. We find that in simulations with a symmetric 1% per year increase and decrease in atmospheric CO₂ the TCRE is larger on the upward than on the downward CO₂ trajectory, suggesting that positive CO₂ emissions are more effective at warming than negative emissions are at subsequently cooling. We also find that the cooling effectiveness of negative CO₂ emissions decreases if applied at higher atmospheric CO₂ concentrations.