A separation apparatus for carbon dioxide is provided which includes an absorption unit for absorbing flue gas from a fossil-fueled power station, a desorption unit and a heat exchanger which on the primary feed side is connected via an inlet-side feedback line to the desorption unit, and on the discharge side is connected via an outlet-side feedback line to the absorption unit. On the secondary feed side, the heat exchanger is connected via an inlet-side feed line to the absorption unit, and on the discharge side is connected via an outlet-side feed line to the desorption unit. A first bypass line connects the inlet-side feedback line to the outlet-side feed line so that a mostly closed first circuit with the desorption unit is formed, and a second bypass line connects the inlet-side feed line to the outlet-side feedback line so a mostly closed second circuit with the absorption unit is formed.