  The underlying distribution of galaxies' dust SEDs (i.e., their spectra
re-radiated by dust from rest-frame $\sim$3$\mu$m-3mm) remains relatively
unconstrained due to a dearth of FIR/(sub)mm data for large samples of
galaxies. It has been claimed in the literature that a galaxy's dust
temperature -- observed as the wavelength where the dust SED peaks
($\lambda_{peak}$) -- is traced most closely by its specific star-formation
rate (sSFR) or parameterized 'distance' to the SFR-M$_\star$ relation (the
galaxy 'main sequence'). We present 0.24" resolved 870$\mu$m ALMA dust
continuum observations of seven $z=1.4-4.6$ dusty star-forming galaxies (DSFGs)
chosen to have a large range of well-constrained luminosity-weighted dust
temperatures. We also draw on similar resolution dust continuum maps from a
sample of ALESS submillimeter galaxies from Hodge et al. (2016). We constrain
the physical scales over which the dust radiates and compare those measurements
to characteristics of the integrated SED. We confirm significant correlations
of $\lambda_{peak}$ with both L$_{IR}$ (or SFR) and $\Sigma_{\rm IR}$
($\propto$SFR surface density). We investigate the correlation between
$\log_{10}$($\lambda_{peak}$) and $\log_{10}$($\Sigma_{\rm IR}$) and find the
relation to hold as would be expected from the Stefan-Boltzmann Law, or the
effective size of an equivalent blackbody. The correlations of $\lambda_{peak}$
with sSFR and distance from the SFR-M$_\star$ relation are less significant
than those for $\Sigma_{\rm IR}$ or L$_{IR}$; therefore, we conclude that the
more fundamental tracer of galaxies' luminosity-weighted integrated dust
temperatures are indeed their star-formation surface densities in line with
local Universe results, which relate closely to the underlying geometry of dust
in the ISM.
