Average ﹩{\rm{\Delta }}{\chi }^{2}﹩ contours of the SINGS sample, excluding warm excess galaxies. The average value is ﹩\overline{{T}_{s}}=81﹩ K with an average power-law index of ﹩\overline{n}=4.8﹩. Using these parameters, ﹩{M}_{{{\rm{H}}}_{2}}(\gt 81\,{\rm{K}})/{M}_{{{\rm{H}}}_{2},\mathrm{total}}=15 \% ﹩ of the ﹩{{\rm{H}}}_{2}﹩ mass is probed directly via rotational emission (Section 4.2.3).