The measuring system includes a transducer apparatus with two tubes. Each tube is adapted to be flowed through by a fluid from an inlet end toward an outlet end and to be caused to vibrate. An electromechanical exciter mechanism excites and 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 the tube, wherein each of the temperature sensors registers a measuring point temperature, and converts such into a temperature measurement signal temperature. A measuring and operating electronics (ME) generates a transducer temperature measured value representing a transducer apparatus temperature so that a magnitude of the transducer temperature measured value is greater than a magnitude of the measuring point temperature and less than a magnitude of the measuring point temperature.