Introduction  The acoustic tomography （AT） is regarded to be a promising tomography method for temperature distribution measurement， and improving the reconstruction accuracy plays a crucial role in actual applications of the technology.

  Method  This paper proposed a two-stage reconstruction method. First，the original measurement domain was divided into a group of coarse grid elements to reduce the number of the unknown variables and to alleviate the ill-posed nature of the inverse problem in the AT temperature distribution measurement. A new cost function was proposed to convert the AT inverse problem into an optimization problem，which was solved by the Nelder-Mead simplex algorithm to get the temperature distribution on coarse grid elements. In the second stage，the measurement domain was further divided into finer discrete grid elements，and the extreme learning machine was deployed to predict the temperature distribution on the grid elements.

  Result  Numerical simulation results indicate that the proposed reconstruction algorithm not only ensures the numerical stability of the inverse problem in the AT temperature distribution measurement， but also improves the reconstruction accuracy.

  Conclusion  The research findings provide an effective method for the numerical solution of the inverse problem in the AT temperature distribution measurement and the improvement in the reconstruction accuracy.