A measuring system includes a measuring and operation electronic unit (ME) and a transducer device electrically coupled thereto. The transducer device (MW) has at least one tube, through which fluid flows during operation and which is caused to vibrate meanwhile, a vibration exciter, two vibration sensors for generating vibration signals, and two temperature sensors for generating temperature measurement signals (θ1, θ2). The temperature sensors are coupled to a wall of the tube in a thermally conductive manner. The ME is designed to feed electrical power into the at least one vibration exciter to cause mechanical vibrations of the tube by an electrical excitation signal. The ME generates a mass flow sequence representing the instantaneous mass flow rate (m) of the fluid, so that, at least for a reference mass flow rate, the mass flow measurement values are independent of the temperature difference.