  We present a new method for recovering the kinetic temperature of the
intervening diffuse gas to an accuracy of 10%. The method is based on the
comparison of unsaturated absorption-line profiles of two species with
different atomic weights. The species are assumed to have the same temperature
and bulk motion within the absorbing region. The computational technique
involves the Fourier transform of the absorption profiles and the consequent
Entropy-Regularized chi^2-Minimization [ERM] to estimate the model parameters.
The procedure is tested using synthetic spectra of CII, SiII and FeII ions. The
comparison with the standard Voigt fitting analysis is performed and it is
shown that the Voigt deconvolution of the complex absorption-line profiles may
result in estimated temperatures which are not physical. We also successfully
analyze Keck telescope spectra of CII1334 and SiII1260 lines observed at the
redshift z = 3.572 toward the quasar Q1937--1009 by Tytler {\it et al.}.
