A thermal flow meter for measuring a flow rate of a gas includes: a measurement channel for guiding the gas between a channel inlet and a channel outlet; a thermal flow sensor disposed in the measurement channel; a density sensor including an oscillator operable to be acted upon by the gas; a temperature sensor element configured to determine a gas temperature; a pressure sensor element configured to determine a gas pressure; and a measuring-operating circuit configured to: determine a density value of the gas based on a natural frequency of the oscillator; identify a composition of the gas based on the density value, the gas pressure, and the gas temperature; and as a function of the composition, output a flow rate measured value corrected with respect to a cross-sensitivity of the flow rate to the composition of the gas based on flow rate-dependent signals of the thermal flow sensor.