For monitoring the tube arrangement, the measuring system of the invention includes, connected to the transmitter electronics, a temperature measuring arrangement having a first temperature sensor for producing a temperature signal dependent on a temperature of a first of the measuring tubes of the tube arrangement and at least a second temperature sensor for producing a temperature signal dependent on a temperature of a second of the measuring tubes of the tube arrangement. In the method of the invention, it is provided that, in the case of medium flowing through the tube arrangement, a temperature difference existing between the at least two measuring tubes as a result plugging is ascertained and, in case the ascertained temperature difference deviates from a predetermined limit value for the temperature difference representing a non-plugged tube arrangement, a partial plugging of the tube arrangement, especially a plugging of exactly one of the measuring tubes, is signaled.