The equilibrium carbon storage capacity of the terrestrial biosphere has been investigated by running the Lund–Potsdam–Jena Dynamic Global Vegetation Model to equilibrium for a range of CO2 concentrations and idealized climate states. Local climate is defined by the combination of an observation-based climatology and perturbation patterns derived from a 4 × CO2 warming simulations, which are linearly scaled to global mean temperature deviations, ΔTglob. Global carbon storage remains close to its optimum for ΔTglob in the range of ±3°C in simulations with constant atmospheric CO2. The magnitude of the carbon loss to the atmosphere per unit change in global average surface temperature shows a pronounced nonlinear threshold behavior. About twice as much carbon is lost per degree warming for ΔTglob above 3°C than for present climate. Tropical, temperate, and boreal trees spread poleward with global warming. Vegetation dynamics govern the distribution of soil carbon storage and turnover in the climate space. For cold climate conditions, the global average decomposition rate of litter and soil decreases with warming, despite local increases in turnover rates. This result is not compatible with the assumption, commonly made in global box models, that soil turnover increases exponentially with global average surface temperature, over a wide temperature range.