A process for cooling down a hot flue gas stream comprising water vapour and carbon dioxide, the process including: (a) heat exchange between the hot flue gas stream and a cooling water stream so that the hot flue gas stream is cooled to a cooled down gas stream at a temperature at which at least part of the water vapour therein has condensed and the cooling water stream increases in temperature; (b) combining the condensed water vapour and the cooling water stream to produce a combined water stream; (c) separation of the cooled down gas stream from the combined water stream; (d) cooling the combined water stream by contact with air from the atmosphere and by evaporation of a portion of the combined water stream; (e) using at least part of any non-evaporated and cooled water of the combined water stream as at least part of the cooling water stream for cooling the hot flue gas stream in step (a); and (f) storing any non-evaporated and cooled water of the combined water stream that is not used in step (e) and using the stored water later as at least part of the cooling water stream in step (a).