The temperatures in a cylindrically symmetrical transparent plasma in local thermodynamic equilibrium have been determined at low temperatures for low degrees of ionization by using calculated and measured relative intensities of a spectral line. An analytical method is given for the relative intensities of a spectral line as a function of the discharge-channel axis temperature. The relative intensities of a spectral line as a function of time in a transient spark discharge were determined experimentally by using time-resolving spectroscopic techniques. The two sets of intensity data were normalized to unity and the axis temperature was then determined as a function of the discharge time. In the calculations, we used an experimentally established radial temperature distribution function.