<p>The reversibility of climate change has seen much discussion – in particular through consideration of scenarios that overshoot a warming target before being cooled through carbon sequestration. The uptake of heat into the deep ocean during warming can result in a lag in the response of global and local climate when warming is reversed. The impact of ocean heat uptake on climate reversibility can be efficiently investigated using an idealised abrupt transition from pre-industrial atmospheric CO₂ concentrations to four times pre-industrial levels followed by an abrupt transition back to pre-industrial levels. New multi-centennial simulations are undertaken, using the HadGEM3-GC3.1-LL climate model, in which abrupt transitions to pre-industrial conditions are simulated after 25, 100, 250 and 1000 years from the start of the existing instantaneous abrupt-4xCO2 CMIP6 experiment. These simulations result in an increasing amount of heat being input to the ocean, which is subsequently released during the cooling phase. We show that the loss of heat from the ocean in the cooling phase is slower than the heat uptake during warming, with the climate, on a multi-centennial timescale, tending towards a warmer state than the pre-industrial control. During the warm state, the Arctic undergoes Atlantification and, after the cooling phase, returns to a quasi-equilibrium state with greater poleward transport of Atlantic water. The Southern Ocean becomes more isolated from the global system during warming and takes up considerable local heat, which is vented through sustained deep convection during cooling. In neither polar region does the sea ice return to its pre-industrial state, and thus we find that the climate system is not readily reversible for high warming levels. This will have implications for climate overshoot in the real world if warming is not controlled.</p>