This paper discusses a novel technique of estimating gas temperatures based on impedance tomography. More specifically, assume that we have a gas funnel (e.g. doorway, window, chimney) equipped with a mesh of thin electrically conducting filaments. Furthermore, assume that the thermal and thermoelectric properties of the conducting material are known. The temperature mapping method is based on changes of the resistivity of the filaments by the changes in temperature. The inverse problem is closely related to the standard tomography problem. Due to the severe underdetermination of the problem, common inversion techniques used in computerized tomography cannot be employed here. The problem is, therefore, recast in a form of a Bayesian parameter estimation problem. Markov chain Monte Carlo methods (MCMC) are applied for exploring the posterior distribution.