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Land surface temperature (LST) with fine spatiotemporal resolution is a much-needed parameter in the earth’s surface system. The LST downscaling is an efficient way to improve the spatiotemporal resolution of LST and has been developed rapidly in recent years. Due to the simple operations and discernable effects of statistical regression and its extension algorithms, these algorithms have been widely researched. However, most statistical regression models assume scale invariance, which makes the downscaled LST inaccurate. This study analyzed the scale effect in the process of LST upscaling/downscaling, then proposed a new algorithm based on Taylor expansion for Moderate Resolution Imaging Spectroradiometer (MODIS) LST downscaling. The Taylor expansion algorithm estimates regression coefficients between LST and auxiliary parameters in the consistent scale. It is tested in three typical areas of different landscapes with different auxiliary parameters, and the results are significantly improved compared to the traditional algorithm. However, the new algorithm may introduce the temporal discrepancy between MODIS LST and empirical concavity factor ($S$), which is estimated with Landsat 8 data, into the downscaling procedure in some circumstances. To discuss the influence of temporal discrepancy, we designed three schemes for pairing MODIS and $S$ and analyzed the downscaled results. The results show that the proposed algorithm got the best downscaled results when the MODIS LST acquired time is consistent with the time of $S$. When the time is inconsistent, the pairing scheme of a similar season gives better results than that of different seasons. The algorithm performs generally well so long as the spatial distribution of auxiliary parameters in the date of Landsat 8 acquisition is similar to the date of MODIS acquisition. [ABSTRACT FROM AUTHOR]