As the likelihood of temporarily exceeding 1.5 °C of global warming rises, understanding the response of the ocean-climate system to overshooting this warming level is of increasing importance. Here, we apply the Adaptive Emissions Reduction Approach to the Earth System Model GFDL-ESM2M to conduct novel overshoot scenarios which temporarily exceed 1.5 °C of global warming to 2.0, 2.5 and 3.0 °C, alongside a complementary scenario that stabilizes global temperature at 1.5 °C. The simulation framework allows to isolate impacts attributable to the temperature overshoots alone, both during their peaks and after their reversals, in simulation timeframes spanning from 1861 to 2500. Our results reveal that, while global sea surface temperatures eventually retrace to 1.5 °C stabilization levels, substantial residual ocean surface warming persists regionally, particularly in the North Atlantic (regional average of up to +3.1 °C in the 3°C overshoot scenario) and the Southern Ocean (+1.2 °C). The residual warming is primarily attributed to the recoveries of the Atlantic and Southern Ocean meridional overturning circulation, resulting in a reversed pattern of disproportionate surface warming in low-latitude oceans found during the transient peak of the overshoot. Excess subsurface heat storage in low and mid-latitudes furthermore prevents steric sea level rise from reverting to 1.5 °C stabilization levels in any overshoot scenario, with sea level remaining up to 32 % higher in the 3 °C overshoot scenario. Both peak overshoot impacts and persistent changes following overshoot reversal bear significant implications for future assessments of coastlines, regional climates, marine ecosystems, and ice sheets.

High-latitude frozen soils contain a vast store of organic matter, a potential source of greenhouse gases due to permafrost thaw. Understanding natural carbon cycle responses to climate change is crucial for emission reduction strategies. We use the Max Planck Institute Earth System Model, driven by the Adaptive Emission Reduction Approach (AERA) and accounting for the impact of frozen soil carbon (FSC), to assess emission pathways and remaining emissions budgets for limiting global warming to 2°C and 3°C relative to preindustrial levels. We found that thawing FSC adds 122 PgC under 2°C and 229 PgC under 3°C warming, available for decomposition in active layer, with about 75% reaching the atmosphere as carbon-dioxide by 2300. Emission pathways that include the release of FSC diverge from their respective reference simulations without permafrost by the middle and end of the current century. By 2300, remaining budgets are reduced by ~13% (115 PgC) for 2°C and ~11% (156 PgC) for 3°C stabilization levels. Annual permafrost emissions average ~0.7 PgC/yr for 3°C and ~0.3 PgC/yr for 2°C scenarios. However, temporary emission peaks reaching half of present-day annual fossil fuel emissions (~5 PgC) are possible. Surprisingly, while negative emissions are required for both reference simulations, only the simulation for the 3°C warming, accounting for FSC, requires negative fossil fuel emissions. This occurs because the FSC release causes an earlier initiation of emission reduction by AERA, resulting in a smoother emission curve. These findings underscore the importance of factoring in permafrost thaw in mitigation action.