  We used FIR and submillimeter continuum data from Herschel and the Atacama
Pathfinder EXperiment (APEX) to fit pixel-by-pixel modified Planck SEDs to
prestellar and protostellar clumps in the Census of High- and Medium-mass
Protostars (CHaMP) ($280^{\circ}<\ell<300^{\circ}$, $-4^{\circ}<b<+2^{\circ}$).
We present maps of dust temperature ($T_{\text{d}}$) and H$_2$ column density
(\ncol) for molecular clumps in the Carina Nebula complex (Regions 9 through
11), and surrounding RCW 64 (Region 26). We compare the column densities of CO
and H$_2$ to chart regional variations in their correspondence, and derive maps
of the CO abundance. We find the CO abundance varies by an order of magnitude
or more across each region, averaging a few$\times$10$^{-5}$ CO per H$_2$, and
that the CO abundance distribution across each clump is correlated in both form
and magnitude with environmental conditions, especially $T_{\text{d}}$. This
demonstrates that no single CO abundance suffices to convert from
$N_{\text{CO}}$ to \ncol, even within a single molecular cloud. We also find
that $L/M$ traces $T_{\text{d}}$ almost exclusively, and therefore is not an
independent star formation tracer, but minima in $T_{\text{d}}$ almost
universally coincide with maxima in \ncol, implying that cooling and density
enhancement must be simultaneous steps in prestellar clump evolution. Finally,
based on generalized histogram N-PDFs of clump-scale (1-5 pc) and cloud-scale
($\gtrsim10$ pc) samples, we could only obtain dual log-normal and power-law
fits to $\sim10\%$ of the clumps. The physical parameters derived from these
fits approach theoretical expectations, but have largely unknown uncertainties,
so we advise treating the results of N-PDF fitting with caution.
