The elimination of time-lag effects is a crucial step in enhancing the correlation between thermal displacement and temperature of long-span bridges, and improving the reliability of displacement-based structural operation damage identification. The fixed time translation method cannot capture the changes in time lags over time and is difficult to completely eliminate time-lag effects. This article uses functional data analysis methods to transform the elimination of time-lag effects into finding an optimal warping function to align thermal displacement and temperature, and proposes an adaptive elimination method for time-lag effects in thermal displacement monitoring data. Firstly, the mechanism of time-lag effects was revealed through numerical simulation. Secondly, an adaptive elimination method for time-lag effects based on phase-amplitude separation of functional data was introduced. Thirdly, the effectiveness of this method was verified using long-term monitoring data of expansion joint displacement and temperature of a large-span rail-cum-road bridge. Finally, a strategy was presented to cope with the end effect of the adaptive elimination method. The research results indicate that the thermal inertia effect formed by low thermal conductivity is the intrinsic reason for the generation of time-lag effects. The adaptive elimination method of time-lag effects can automatically find the optimal warping function for time-lag effects elimination according to the degree of time lags. The proposed method is significantly better than the fixed time translation method. The strategy of data extension can effectively remove the end effect and achieve complete elimination of time-lag effects.