Brightness temperature inversion is one of the most essential tasks in satellite remote sensing data processing. Accurate calculation of brightness temperature is crucial for many remote sensing applications, such as land surface temperature retrieval, sea surface temperature retrieval, and active fire detection. Due to the huge amount of remote sensing data, performance is also very important for operational use. Major current approaches for brightness temperature inversion are iteration methods, Look-Up-Table (LUT) methods, and empirical formula methods. Some of these algorithms can invert brightness temperature efficiently with limited accuracy, while others can invert brightness temperature at high accuracy but have lower performance. It is desirable to develop an algorithm that can make the balance of accuracy and performance more flexible and can invert brightness temperature efficiently even at high accuracy. In this paper, we analyse the advantages and limitations of the current algorithms for brightness temperature inversion, and propose a new approach based on the high-order approximation of the relationship between band-averaged radiance and brightness temperature. Our approach has the advantages of high accuracy and flexibility. It can be vectorized easily to exploit the advanced features of current computing platforms and improve performance in operational data processing. For validation and analysis, we have applied this method to brightness temperature inversion of MODIS thermal infrared (TIR) measurements and compared with other algorithms for accuracy and performance. The results demonstrate that our approach can be used for operational data processing more flexibly and efficiently.