The invention relates to a measuring system, which comprises a transducer device (MW) having two tubes (11, 12), each of which has a lumen (11') surrounded by a wall, in particular a metal wall, and which extend from respective inlet-side ends (11a, 12a) to respective outlet-side ends (11b, 12b) and which are each designed for the flow of a fluid therethrough from the respective inlet-side ends toward the respective outlet-side ends and for being vibrated during said flow. An electromechanical exciter assembly formed by means of at least one vibration exciter (41) is used to excite and maintain mechanical vibrations of each of the tubes about an associated static resting position, and a sensor assembly (S) formed by means of at least one vibration sensor (51) is used to sense mechanical vibrations of at least one of the tubes (11, 12). In addition, the transducer device has two temperature sensors (71, 72), wherein each of the temperature sensors (71, 72) is coupled mechanically yet in a thermally conductive manner to a wall of the tube (11) and wherein each of the temperature sensors (71, 72) is designed to sense a measurement-point temperature (θ1, θ2), namely a temperature of the wall of the tube (11) at a temperature measurement point formed by means of the temperature sensor (71; 72), and to convert said measurement-point temperature into a temperature measurement signal (Θ1, Θ2), namely an electrical measurement signal representing the measurement-point temperature. In addition, the temperature sensor (71) is positioned at a smaller distance from end (11a) than from end (11b), while the temperature sensor (72) is positioned at a smaller distance from end (11b) than from end (11a). In addition, a measuring and operating electronic unit (ME) of the measuring system, which is electrically coupled to the transducer device, is designed to generate a transducer temperature measurement value by using the temperature measurement signals (Θ1, Θ2), which transducer temperature measurement value represents a transducer device temperature, which deviates both from measurement-point temperature (θ1) and from measurement-point temperature (θ2), in such a way that the magnitude of said transducer temperature measurement value is greater than the magnitude of measurement-point temperature (θ1) yet less than the magnitude of measurement-point temperature (θ2).