Light field camera can solve the problems of complex optical path and difficult synchronous trigger of radiation temperature measurement multi camera system, which has some unique advantages in three-dimensional temperature reconstruction of radiation imaging. The LSQR is a classical algorithm for solving the least square problem based on large sparse matrix. When the algorithm is used to reconstruct three-dimensional temperature field, it depends on the initial value of temperature, and the reconstruction accuracy is not ideal when the signal-to-noise ratio is low. In this paper, a damped LSQR-LMBC reconstruction algorithm is proposed. By adding a damped regularization term into the LSQR method, the anti noise performance of flame three-dimensional temperature field reconstruction is improved. By combining the LMBC algorithm, the absorption coefficient and three-dimensional temperature field are solved at the same time. In the numerical simulation part, with the gradual reduction of signal-to-noise ratio, the reconstruction effect of Damped LSQR turns more stable than LSQR. When the signal-to-noise ratio reaches 13.86 dB, the reconstruction accuracy is improved by about 30%. The average reconstruction error of damped LSQR-LMBC is 6.63%. The three-dimensional temperature field distribution of butane flame is consistent with the characteristic of radiation flame combustion. Compared with the temperature measurement data of thermocouple, the relative error is about 6.8%.