  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 (CHESS) 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
$\beta^{1}$ Scorpii ($\beta$ Sco) and $\gamma$ Arae. We present flight results
of interstellar molecular hydrogen (H$_{\rm 2}$) 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$^{\prime \prime}$ H$_{\rm 2}$ absorption features (Savage et al. 1977).
For $\beta$ Sco, we find that the derived column density of the J$^{\prime
\prime}$ = 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$^{\prime \prime}$ = 1
absorption wing, increasing the inferred column density in the previous work.
We extend this analysis to 9 $Copernicus$ and 13 $FUSE$ spectra to explore the
interdependence of the column densities of different rotational levels and how
the H$_{\rm 2}$ kinetic temperature is influenced by these relationships. We
find a revised average gas kinetic temperature of the diffuse molecular ISM of
T$_{01}$ = 68 $\pm$ 13 K, 12% lower than the value found previously.
