A method for separating CO2 from combustion exhaust gas includes discharging the CO2-containing combustion exhaust gas mass flow into the carbonator of a carbonate looping system having at least one carbonator and one calciner. Combining the CO2 of the combustion exhaust gas mass flow with a carbonate-forming sorbent inside the carbonator to form a carbonate. Sending the carbonate as a carbonate-solids mass flow is sent to the calciner. Burning the carbonate at the carbonate-specific calcination temperature by the addition of heat provided by an additional firing that uses oxygen as the oxidant, whereby regenerated sorbent and a gas essentially containing CO2 is formed. Sending the hot regenerated sorbent to the carbonator as a sorbent-solids mass flow for carbonization of CO2, and discharging the hot gas as gas mass flow. Replacing at least a portion of the heat of the additional firing with heat removed from the carbonate-solids mass flow or the gas mass flow in one or more heat exchangers prior to its entry into the calciner or inside the calciner.