A realistic representation of the Southern Ocean (SO) in climate models is critical for reliable global climate projections. However, many models are still facing severe biases in this region. Using a fully coupled global climate model at non-eddying (1/2∘) and strongly eddying (1/10∘) grid resolution in the SO, we investigate the effect of a 0.5 °C, 1.0 °C and 1.6 °C warmer than observed SO on i) the spin-up behaviour of the high-resolution simulation, and ii) the representation of main dynamical features, i.e., the Antarctic circumpolar current (ACC), the subpolar gyres, the overturning circulation and the Agulhas regime in a quasi-equilibrium state. The adjustment of SO dynamics and hydrography critically depends on the initial state and grid resolution. When initialised with an observed ocean state, only the non-eddying configuration quickly builds up a strong warm bias in the SO. The high-resolution configuration initialised with the biased non-eddying model state results in immense spurious open ocean deep convection, as the biased ocean state is not stable at eddying resolution, and thus causes an undesirable imprint on global circulation. The SO heat content also affects the large-scale dynamics in both low- and high-resolution configurations. A warmer SO is associated with a stronger Agulhas current and a temperature-driven reduction of the meridional density gradient at 45∘S to 65∘S and thus a weaker ACC. The eddying simulations have stronger subpolar gyres under warmer conditions while the response in the non-eddying simulations is inconsistent. In general, SO dynamics are more realistically represented in a mesoscale-resolving model at the cost of requiring an own spin-up.