A thermal flow-rate sensor includes: a first temperature sensor that detects the temperature at a specified location of the outer-wall surface of a pipe; a heat-transfer element that is arranged on the outer-wall surface of the pipe in a state separated from the first temperature sensor, and that exchanges heat with a measurement medium by heating or cooling the outer-wall surface of the pipe; a second temperature sensor that detects the temperature of a portion of the outer-wall surface of the pipe that is heated or cooled by the heat-transfer element; and a control unit that performs specified processing. A heat-flux sensor is arranged between the heat-transfer element and the outer-wall surface of the pipe and directly detects heat flux between the heat-transfer element and the pipe; and the control unit detects the flow rate of the measurement medium based on the temperature that is directly detected by the first temperature sensor, the temperature that is detected by the second temperature sensor, and the heat flux that is detected by the heat-flux sensor.