Abstract Solutions including oscillatory responses to monotonic forcing are derived for a generalized energy balance box model, and used to help explore general circulation model (GCM) global surface temperature responses to CO2 ${\text{CO}}{2}$ forcing. Oscillations superposed on the warming following abrupt CO2 ${\text{CO}}{2}$ increases are observed in several GCMs. They are associated with a cooling of the North Atlantic, linked to strong changes in the Atlantic Meridional Overturning Circulation (AMOC) and Arctic sea ice in GCM simulations. Global temperature plateaus lasting for decades in abrupt CO2 ${\text{CO}}{2}$ quadrupling experiments are linked to an AMOC collapse to a weak state of 2–7 Sv. In the abrupt CO2 ${\text{CO}}{2}$ doubling experiment of a long CESM1 run, allowing AMOC to recover, we find oscillations in both temperature and AMOC persisting over multi‐century timescales. A box model fitted to this predict oscillations superposed on future long‐term warming too, with amplitudes around some tenths of a degree.

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