This study developed a new methodology for measuring and predicting the time variance of the relative displacement between two prefabricated segments during bridge construction to expedite the construction process. In particular, the methodology enables the automated estimation of the relative displacement between two bridge segments. The methodology was applied during the construction of the Cheonsa Bridge in South Korea. First, a terrestrial laser scanner was used to extract the 3D positions of two bridge segments (Segments 17 and 20) simultaneously. Then, the 3D positions of the two segments were monitored over the course of two days to estimate the variation in the relative displacement between the two segments due to daily thermal loading. Given that Segment 18 is attached to Segment 17, the relative displacement between Segments 18 and 20 was predicted based on the displacement between segments 17 and 20. Subsequently, the optimal dimensions of the key segment (Segment 19) to be installed between Segments 18 and 20 were determined, and the key segment was fabricated accordingly. By processing the installment of Segment 18 and the fabrication of Segment 19 in parallel, the construction time of the Cheonsa Bridge was reduced by 10 days.