A system for measuring fluid flow in a wellbore is provided. A probe includes at least a heater. A fiber optic cable is connected to the probe. The system is programmed to perform operations including: changing an output of the heater to thereby change a temperature of drilling fluid moving over a fiber optic cable; measuring a strain on the fiber optic cable caused by changing the temperature of the drilling fluid; preliminarily determining a velocity of the drilling fluid from the measured strain; measuring at least a second parameter of the drilling fluid; adjusting the preliminary determined velocity based on the measured at least a second parameter to yield an adjusted velocity; and determining a flow rate of the drilling fluid based on the adjusted velocity.