Described is an apparatus (5) as well as a method for cooling kiln exhaust gases in a kiln bypass (7), which apparatus comprises a mixing chamber (9) for extracting and cooling a portion of the kiln exhaust gases from a kiln system (1, 3), said mixing chamber (9) comprising a tubular housing being provided at one end with an exhaust gas inlet (11) for kiln exhaust gases and provided at its other end with an outlet (13) for cooled exhaust gases, said mixing chamber (9) further comprising a tangential inlet (15) for cooling gases, where the apparatus also comprises a first fan (17) for supplying cooling gases to the mixing chamber (9) and a second fan (19) for drawing the kiln exhaust gases through the kiln bypass (7). The apparatus (5) and the method is peculiar in comprising means (31, 33) for measuring, respectively, the mass flow mA and the flow velocity vA of the cooling gases which are introduced to the mixing chamber (9), and the mass flow mB and the flow velocity vB of the cooled exhaust gases being discharged from the mixing chamber (9), a calculating unit (35) to determine on the basis of the measured values mA, vA, mB and vB the actual mass flow mC and the flow velocity vC for the kiln exhaust gases being drawn through the kiln bypass (7) and to compare the actual mass flow mC with a predetermined value for kiln exhaust gases targeted for being drawn through the kiln bypass (7), a calculating unit (35) to determine on the basis of the values mA, vA, mC and vC the actual swirl number S of the gases in the mixing chamber (9) and to compare this with a predetermined, desired value for the swirl number of the gases in the mixing chamber (9), and means (37, 39, 41) for regulating respectively the fan (17) for feeding cooling gases to the mixing chamber (9), the fan (19) for drawing the kiln exhaust gases through the kiln bypass (