This paper demonstrates a hyperspectral tomographic technique that can recover the temperature and concentration field of gas flows based on multi-mode absorption spectroscopy (MUMAS). This method relies on the recently proposed concept of nonlinear tomography, which can take full advantage of the nonlinear dependency of MUMAS signals on temperature and enables 2D spatial resolution of MUMAS which is naturally a line-of-sight technique. The principles of MUMAS and nonlinear tomography, as well as the mathematical formulation of the inversion problem, are introduced. Proof-of-concept numerical demonstrations are presented using representative flame phantoms and assuming typical laser parameters. The results show that faithful reconstruction of temperature distribution is achievable when a signal-to-noise ratio of 20 is assumed. This method can potentially be extended to simultaneously reconstructing distributions of temperature and the concentration of multiple flame species.