The study of soft X-ray solar emission lines based on the temperature-modified Coulomb potential, presented in two earlier papers, is pursued further. Specifically, we attempt to calculate the relative intensities of the most intense lines in the SL 304 solar coronal data in a ''minimal'' framework wherein we give a complete determination of the eigenfunctions of the finite-temperature Schrodinger equation, the transition matrix elements, and the formulae for the line intensities of the emission spectra, but make suitable simplifying assumptions with regard to the populations of the relevant eigenstates of that equation and the transfer of line radiation. Our results do not negate the possibility of the existence of ''hot'' hydrogen and suggest that the spectroscopy of such a system may prove useful as a supplement to the conventional approach.