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We report high resolution observations of the $^{12}$CO$(1\rightarrow0)$ and$^{13}$CO$(1\rightarrow0)$ molecular lines in the Carina Nebula and the Gum 31region obtained with the 22-m Mopra telescope as part of the The Mopra SouthernGalactic Plane CO Survey. We cover 8 deg$^2$ from $l = 285^{\circ}$ to290$^{\circ}$, and from $b = -1.5^{\circ}$ to +0.5$^{\circ}$. The molecular gascolumn density distributions from both tracers have a similar range of values.By fitting a grey-body function to the observed infrared spectral energydistribution from Herschel maps, we derive gas column densities and dusttemperatures. The gas column density has values in the range from $6.3\times\10^{20}$ to $1.4\times 10^{23}$ cm$^{-2}$, while the dust temperature hasvalues in the range from 17 to 43 K. The gas column density derived from thedust emission is approximately described by a log-normal function for a limitedrange of column densities. A high-column density tail is clearly evident forthe gas column density distribution, which appears to be a common feature inregions with active star formation. There are regional variations in thefraction of the mass recovered by the CO emission lines with respect to thetotal mass traced by the dust emission. These variations may be related tochanges in the radiation field strength, variation of the atomic to moleculargas fraction across the observed region, differences in the CO moleculeabundance with respect to H$_{2}$, and evolutionary stage differences of themolecular clouds that compose the Carina Nebula-Gum 31 complex.

The Carina Nebula and Gum 31 molecular complex: I. Molecular gas distribution, column densities and dust temperatures