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Sea surface temperature (SST) is an essential climate variable that can be used to assess climate change. One kind of method commonly used to estimate SST based on remote-sensing measurements is the split-window (SW) algorithm. However, the derivation of the linear SW algorithm does not appear to reflect reality because some assumptions and approximations were used. Moreover, the quadratic SW equation cannot be interpreted theoretically although it maintains the structure of the linear SW equation. The Gaofen-5 (GF-5) satellite launch is planned for 2018. Focusing on exploring the mechanism of the SW algorithm using GF-5 data, this study investigated the assumptions and approximations used to derive the linear SW technique. Two revised equations of these assumptions and approximations were developed. Combining the revised equations, a nonlinear SW algorithm was obtained that could be simplified to the quadratic equation. Compared with previous research, this study focuses more on the theoretical interpretation and improves our understanding of the semi-empirical quadratic SW equation. The matchup data set produced by the European Organization for the Exploitation of Meteorological Satellites Ocean and Sea Ice Satellite Application Facility was used to validate the quadratic SW algorithm. A bias of -0.05K and a RMSE of 0.53K were obtained.