System to capture CO 2 from a combustion flue gas using a CaO/CaCO 3 chemical loop comprising at least the following elements: i) one or more combustion chamber (50, 57, 58) burning a fuel with air and generating a high temperature flue gas, wherein at least a combustion chamber is connected to a carbonator by means of a first pipe, ii) a second pipe supplying a solid stream rich in CaO to the carbonator to react with the CO 2 contained in the high temperature flue gas and form carbonated solids, iii) a third pipe to extract from the carbonator the carbonated solids and the high temperature flue gas depleted in CO 2, iv) a first cyclone connected to the carbonator by means of the third pipe, with said first cyclone separating the high temperature flue gas depleted in CO 2 from the carbonated solids, v) a calciner being fed with carbonated solids by means of a fourth pipe, vi) a fifth pipe to extract the calcined solids and CO 2 rich gases generated in the calciner, when supplied with heat to rise the temperature of the carbonated solids entering through the fourth pipe and drive the endothermic calcination of CaCO 3, vii) a second cyclone connected to the calciner by means of the fifth pipe for separating the CO 2 rich gas from the calcined solids viii) at least a third cyclone to put in direct contact the high temperature flue gas stream generated in the combustion chamber (50, 57, 58) with the calcined solids generated in the calciner, thereby reducing the heat requirements for calcination, ix) a sixth pipe (6, 23) supplying the high temperature flue gas generated in the combustion chamber (50, 57) to the third cyclone, characterized in that the system further comprises: x) a seventh pipe supplying part of the calcined solids from the second cyclone to the sixth pipe (6, 23), wherein the high temperature flue gas generated in the combustion chamber (50, 57) and the calcined solids form the second cyclone are mixed before entering the third cyclone, the calcined solids being overheated by the high temperature flue gas, xi) the third cyclone separating the overheated calcined solids from the high temperature flue gas, and xii) an eighth pipe returning overheated calcined solids to the calciner from the third cyclone. i) one or more combustion chamber (50, 57, 58) burning a fuel with air and generating a high temperature flue gas, wherein at least a combustion chamber is connected to a carbonator by means of a first pipe, ii) a second pipe supplying a solid stream rich in CaO to the carbonator to react with the CO 2 contained in the high temperature flue gas and form carbonated solids, iii) a third pipe to extract from the carbonator the carbonated solids and the high temperature flue gas depleted in CO 2, iv) a first cyclone connected to the carbonator by means of the third pipe, with said first cyclone separating the high temperature flue gas depleted in CO 2 from the carbonated solids, v) a calciner being fed with carbonated solids by means of a fourth pipe, vi) a fifth pipe to extract the calcined solids and CO 2 rich gases generated in the calciner, when supplied with heat to rise the temperature of the carbonated solids entering through the fourth pipe and drive the endothermic calcination of CaCO 3, vii) a second cyclone connected to the calciner by means of the fifth pipe for separating the CO 2 rich gas from the calcined solids viii) at least a third cyclone to put in direct contact the high temperature flue gas stream generated in the combustion chamber (50, 57, 58) with the calcined solids generated in the calciner, thereby reducing the heat requirements for calcination, ix) a sixth pipe (6, 23) supplying the high temperature flue gas generated in the combustion chamber (50, 57) to the third cyclone, x) a seventh pipe supplying part of the calcined solids from the second cyclone to the sixth pipe (6, 23), wherein the high temperature flue gas generated in the combustion chamber (50, 57) and the calcined solids form the second cyclone are mixed before entering the third cyclone, the calcined solids being overheated by the high temperature flue gas, xi) the third cyclone separating the overheated calcined solids from the high temperature flue gas, and xii) an eighth pipe returning overheated calcined solids to the calciner from the third cyclone.