The measurement of combustion temperature fields is of great significance for combustion analysis. The background schlieren method, as a non-intrusive optical measurement technology, has the advantages of simple equipment and full-field measurement, and has been widely used in the reconstruction of combustion temperature field in recent years. However, the traditional background schlieren approach relies on the assumption of a parallel paraxial optical path when solving the light-deflection angle, and its accurate analytical solution cannot be established. This leads to large errors in the reconstruction of non-axisymmetric temperature fields and reduces the traceability of the results. Therefore, this paper proposes a non-axisymmetric temperature field reconstruction method based on the conservation principle of angular momentum. The innovation core of this method lies in introducing the law of conservation of angular momentum into the process of solving deflection of light angle, and constructing a more accurate analytical model for light propagation in complex flow fields. Firstly, the background images with and without flames are analyzed using an image cross-correlation algorithm to obtain speckle displacements from multiple viewing perspectives. Based on the principle of conservation of angular momentum, the deflection of light angle is calculated by selecting the offset data on the same height plane, and the normalized refractive index difference distribution is obtained through Radon inverse transformation. Then, according to the Gladstone-Dale relation between refractive index and gas density, combined with the ideal gas state equation, the refractive index distribution is converted into the corresponding temperature field distribution. The experimental results show that, compared with the traditional methods, the precision of the temperature field reconstructed based on the conservation of angular momentum is significantly improved, especially in the peak areas with the largest temperature gradient. The overall reconstruction error is reduced by about 30%, which can realize the reconstruction of non-axisymmetric temperature fields. The proposed method can effectively improve the accuracy of temperature field reconstruction and expand the application range of background schlieren method.