The measuring system functions to measure at least one measured variable of a flowing fluid and comprises a fluid supply line (60), a converter device (20) which has a tube (21) and at least one tube (22) and is equipped to provide at least one measurement signal (s1) corresponding to the at least one measured variable, a fluid return line (40), and a fluid extraction line (50). According to the invention, initially a first flow path (I) is established which leads from the lumen of the fluid supply line (60) to the lumen of the tube (21), further to the lumen of the tube (22), and further to the lumen of the fluid return line (40), nevertheless not to the lumen of the fluid extraction line (50), and afterward fluid is allowed to flow along said flow path (I), for example, for tempering and/or cleaning parts of the measuring system and/or to condition the fluid. Furthermore, according to the invention, a second fluid path (II) (instead of the first flow path) is established afterwards and which leads from the lumen of the fluid supply line (60) to the lumen of the first tube and parallel to the lumen of the second tube, and further from the lumen of the first tube or from the lumen of the second tube respectively to the lumen of the fluid extraction line, and fluid is allowed to flow along said second flow path (II). Furthermore, at least one measuring signal (s1) is generated during the flow of fluid along the second flow path, optionally also during the flow of the fluid along said first flow path, and said measuring signal is used to determine measurement values for the at least one measured variable.