This report describes the theory and operation of a pulsed-probe anemometer designed to measure steady three-dimensional velocity fields typical of pulmonary tracheo-bronchial airflows. Local velocities are determined by measuring the transport time and orientation of a thermal pulse initiated at an upstream wire and sensed at a downstream wire. The transport time is a reproducible function of velocity and the probe wire spacing, as verified by a theoretical model of convective heat transfer. When calibrated the anemometer yields measurements of velocity accurate to +/- 5 percent and resolves flow direction to within 1 deg at airspeeds greater than or equal to 10 cm/s. Spatial resolution is +/- 0.5 mm. Measured flow patterns typical of curved circular pipes are included as examples of its application.