﹩{\chi }^{2}﹩ distribution for a normal galaxy NGC 5033 (blue) and an excess warm molecular gas galaxy NGC 3627 (red). The minimum ﹩{\chi }^{2}﹩ occurs at a cutoff temperature of 120 K for NGC 3627; however, for the galaxy NGC 5033 the ﹩{\chi }^{2}﹩ curve decreases throughout as the lower temperature is decreased. For temperatures less than 50 K the model shows no change in the flux ratios since temperatures are too cold to occupy rotational energy levels and hence, a constant ﹩{\chi }^{2}﹩ curve.