The CO2 contained in combustion fumes is captured by carrying out at least the following steps in combination: a) a fuel is burned, producing combustion fumes; b) the fumes are placed in contact with an absorbent solution in order to produce CO2-poor fumes and a CO2-laden solution; c) the CO2-laden solution is regenerated in a thermal regeneration column (RE) in order to produce a regenerated absorbent solution and a CO2-rich gaseous effluent (5); and d) the CO2-rich gaseous effluent is cooled in order to obtain a CO2-enriched gaseous fraction which is evacuated, and a liquid fraction, which is heated by heat exchanged with the combustion fumes and then introduced at the head of regeneration column (RE) as reflux (7).