The Mesosphere and Lower Thermosphere (MLT) is a transitional region between the neutral atmosphere and the ionosphere, as well as an important coupling region where many dynamic processes including gravity waves, tidal waves and planetary waves are active. Based on the Mesopause Airglow Spectral Photometer (MASP), a novel instrument developed by our group, this work provides the inversion method in detail for deriving rotational temperature from the emission of the airglow O₂(0-1) band. MASP instrument consists of an aperture, a main achromatic doublet lens, a narrow-band interference filter, an imaging lens and a cooled CCD detector. The optical elements and CCD detector are connected by four black alumina sleeves which are fixed on the optical breadboard by means of several metal supports and precise clasps. The field of view (FOV) for MASP is ±13.6°, and the detection target is a thin airglow layer at an altitude of about 94 km with a thickness of 3~6 km. Thus, the area of the zenith direction projected by the FOV at this altitude is about 44 km in diameter so that MASP is designed to detect the average temperature of this area. Based on the optical principle of MASP, the spectral characteristics of the airglow O₂(0-1) band and the instrument parameters by calibrations, we constructed the forward model to calculate synthetic spectrum from the forward image. We then describe the detailed process of the inversion algorithm, including the eliminations of dark noise, cosmic rays, moonlight images and background scattered signal of the continuous spectrum. In addition, the calculation method of the actual observed synthetic spectrum, the temperature inversion process and the evaluation of the error are provided respectively. The MASP has been conducting routine observations on the field platform of Nanjing University of Information Engineering since September 2018. At present, more than thirty nights of data have been obtained. The observation results in this paper show two whole night observation cases and the mean value averaged by 13 sets of valid data in October 2018. The general trend shows that the observed temperature ranges from 170 to 220 K, and the error ranges from (+1.8 K) to (+4.3 K). Compared with the data of the MSISE-00 empirical model, the temperature trend has a good consistency, which verifies the validity and accuracy of the inversion method. MASP has compact structure, stable performance and easy maintenance. It is thereforesuitable for multi-station networking observation.