Measuring the temperature and abundance patterns of clouds in the interstellar medium (ISM) provides an observational basis for models of the physical conditions within the clouds, which play an important role in studies of star and planet formation. The Colorado High-resolution Echelle Stellar Spectrograph is a far-ultraviolet rocket-borne instrument designed to study the atomic-to-molecular transitions within diffuse molecular and translucent cloud regions. The final two flights of the instrument observed β^1 Scorpii (β Sco) and γ Arae. We present flight results of interstellar molecular hydrogen excitation on the sightlines, including measurements of the column densities and temperatures. These results are compared to previous values that were measured using the damping wings of low J'' H_2 absorption features. For β Sco, we find that the derived column density of the J'' = 1 rotational level differs by a factor of 2–3 when compared to the previous observations. We discuss the discrepancies between the two measurements and show that the source of the difference is due to the opacity of higher rotational levels contributing to the J'' = 1 absorption wing, increasing the inferred column density in the previous work. We extend this analysis to 9 Copernicus and 13 Far-Ultraviolet Spectroscopic Explorer spectra to explore the interdependence of the column densities of different rotational levels and how the H_2 kinetic temperature is influenced by these relationships. We find a revised average gas kinetic temperature of the diffuse molecular ISM of T_(01) = 68 ± 13 K, 12% lower than the value found previously
