In power plant boiler, the temperature field information directly reflects its internal combustion conditions. To ensure the proper running of the whole system and reduce environmental pollution, it is essential to monitor the temperature field inside boiler quickly and accurately. In this paper, a new temperature field reconstruction method based on acoustic thermometry is proposed. First, in order to obtain the temperature of the discrete coarse grid in measurement area, the temperature field reconstruction problem is transformed into an optimization problem, which is solved by the improved monotone fast iterative shrinkage-thresholding algorithm. Then, based on the obtained temperature of coarse grid, the temperature field of the whole measurement area is reconstructed by the kernel extreme learning machine. Compared with existing algorithms, simulation and experimental results show that the proposed method can acquire complete reconstruction results with shorter reconstruction time, better reconstruction accuracy and robustness, and is feasible for engineering applications.