Doppler asymmetric spatial heterodyne spectroscopy is recently developed for spaceborne measurement of middle and upper atmospheric wind field, which relies on the accurate inverse of interferogram phase to calculate the Doppler shift of airglow emission lines. The change of temperature leads the optical and mechanical components to thermally deformed, causing the imaging plane to thermally drift relative to the detector, changing the distribution of interferogram phase on pixels, and directly introducing phase errors to affect the wind speed inversion. In order to reduce the influence of imaging thermal drift on phase inversion, the segmented fitting method is used in this paper to detect the sub-pixel edges of notch patterns and monitor imaging thermal drift accordingly. In the thermal stability test of a near-infrared Doppler asymmetric spatial heterodyne interferometer prototype, the thermal imaging drifts and ambient temperature show a high consistency in the trend of high-frequency oscillation, and the correlation coefficient can reach 0.86 after removing the baseline. After phase correct by using the thermal imaging shift, the high-frequency oscillation of interferogram phase shift is also greatly suppressed. In order to further verify the accuracy of the algorithm, the influence of the data signal-to-noise ratio and the data distribution characteristic parameter errors used in the fitting on the edge detection are simulated. The results show that the edge detection accuracy is restricted mainly by the data signal-to-noise ratio and the accuracy of the fringe frequency parameters. When the error of the fringe frequency parameter used for fitting is less than 0.5%, the error of other data distribution characteristic parameters is less than 5%, and the data signal-to-noise ratio is enhanced more than 35 times, the algorithm in this paper can achieve a detection accuracy higher than 0.05 pixels.