The measuring system comprises a transducer apparatus with two tubes, each having a lumen surrounded by a wall. A fluid flows through each tube, while the tube is vibrated. An electromechanical-exciter mechanism maintains mechanical oscillations of each of the tubes, and a sensor arrangement registers mechanical oscillations of at least one of the tubes. The transducer apparatus includes two temperature sensors, each being mechanically and thermally conductively coupled with a wall of a respective one of the tubes and adapted to register a measuring point temperature and to convert such into a temperature measurement signal. A measuring- and operating electronics is adapted, with application of the temperature measurement signals, to generate a transducer temperature measured value, which represents a transducer apparatus temperature, which deviates both from each of the measuring point temperatures, such that a magnitude of the transducer temperature measured value is between the measuring point temperatures.