Mitigation pathways allowing for temperature overshoot often ignore the related climate and macroeconomic impacts. Net-zero pathways with limited overshoot could reduce low-probability high-consequence risks and economic loss. Mitigation pathways exploring end-of-century temperature targets often entail temperature overshoot. Little is known about the additional climate risks generated by overshooting temperature. Here we assessed the benefits of limiting overshoot. We computed the probabilistic impacts for different warming targets and overshoot levels on the basis of an ensemble of integrated assessment models. We explored both physical and macroeconomic impacts, including persistent and non-persistent climate impacts. We found that temperature overshooting affects the likelihood of many critical physical impacts, such as those associated with heat extremes. Limiting overshoot reduces risk in the right tail of the distribution, in particular for low-temperature targets where larger overshoots arise as a way to lower short-term mitigation costs. We also showed how, after mid-century, overshoot leads to both higher mitigation costs and economic losses from the additional impacts. The study highlights the need to include climate risk analysis in low-carbon pathways.