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A physical modeling and a rigorous theoretical analysis consisting of the two-temperature model and the generalized transmission-line model is used to evaluate a photo-induced terahertz continuous-wave voltage from a dc current-biased high-temperature superconducting (HTS) transmission line by optical heterodyne photomixing. The electrical and optical frequency-response analyses show the amplitude of this voltage increases with increasing beat frequency and decreasing optical frequency of laser beams. Its maximum frequency is found to be limited by the gap frequency of the HTS material, which is consistent with the available experiments reported in the literature. The developed model along with our numerical simulation reveal the ways to produce a coherent traveling-wave and high-power terahertz signal with proper choice of an HTS material, bias condition, geometrical configuration, and parameters of the transmission line and characteristics of two laser beams. This HTS photomixer can play an important role in terahertz transceivers as broadly tunable local oscillators with low-noise/low-power consumption characteristics.