Abstract
Carbon budgets, derived from the near-linear link between cumulative carbon emissions and global warming, guide climate mitigation and adaptation. However, the impact of the pace of reaching a target budget on climate response remains uncertain. Using 29 climate models, we compare scenarios reaching the same carbon emission target slowly or quickly. A faster trajectory produces stronger land warming and greater exposure to extreme heat waves than a slower pathway. Of 46 land regions, 37 (80%) warm more and 39 (85%) experience higher heat wave exposure in the faster case. This arises because the deep ocean cannot absorb heat rapidly, amplifying atmospheric warming. These findings underscore that not only the total emissions but also the pace of emissions critically governs regional climate risks.