The invention is directed to a flow sensor having a heater, two temperature measuring sensors, a heater temperature sensor and a medium temperature sensor. A control circuit is provided which controls the overtemperature of the heater in dependence upon the temperature of the flowing medium. With this arrangement, the influence of the temperature dependency of the following on the sensor characteristic are compensated: viscosity, thermal conductance and thermal capacity of the medium. The relationship between the heater temperature and the temperature of the medium is adjusted in a slightly nonlinear manner by means of special evaluation circuits. In this way, a further improvement of the temperature compensation is obtained.