An apparatus for determining and/or monitoring mass flow of a fluid medium through a pipeline, or through a measuring tube. The apparatus includes two temperature sensors and a control/evaluation unit. The two temperature sensors are arranged in a region of a housing facing the medium and in thermal contact with the medium flowing through the pipeline, or through the measuring tube. A first of the temperature sensors is heatably embodied. A second of the temperature sensors provides information concerning the present temperature of the medium. The control/evaluation unit, on the basis of primary measured variables, such as temperature difference between the two temperature sensors and/or heating power fed to the first temperature sensor, ascertains the mass flow of the medium through the pipeline. The control/evaluation unit, in ascertaining the mass flow, provides a correction value for the mass flow and/or for the primary measured variable and/or for a measured value derived from the primary measured variable. And, the control/evaluation unit, in ascertaining the correction value, takes into consideration heat exchange by forced convection and heat exchange by free convection between the temperature sensors and the medium.