The underlying distribution of galaxies' evolving dust SEDs (i.e. spectrum re-radiated by dust from rest-frame ~3 um - 3 mm) still remains relatively unconstrained due to a dearth of FIR/ (sub)mm data for large samples. 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 or parameterized 'distance' to the SFR-M_star relation (the galaxy 'main-sequence'). We present 0.12" resolved 870 um ALMA dust continuum observations of 7 dusty star-forming galaxies (DSFGs) chosen to have a large range of well- constrained luminosity-weighted dust temperatures (lambda_peak). They span redshifts z=1.4-4.6 and are drawn from the central deep portion of SCUBA-2 coverage in COSMOS with photometry drawn from Spitzer, Herschel, SCUBA-2, and ALMA. We also draw on similar resolution dust continuum maps of DSFGs from ALESS (Hodge et al. 2016) to expand the analysis sample. We constrain dust continuum morphology and the physical scales over which the dust radiates and compare those measurements to characteristics of the integrated SED. The effective radii (R_e) of these galaxies range from 1.6-7.7 kpc, and their morphology is well fit to a Gaussian profile (Sersic index n = 0.62). We confirm significant correlations of lambda_peak (or T_d ) with both L_IR (or SFR) and L_IR / R_e^2 (SFR surface density). Using a galaxy-scale Stefan-Boltzmann-type argument for the relationship between incident radiation heating dust in the ISM, we investigate the correlation between lambda_peak and L_IR / R_e^2. We find a value of the slope of this relation, eta = -0.22, which deviates from the theoretical value of -0.25 by 2.6 sigma. The correlations of lambda_peak with sSFR and distance from the main sequence are less significant; therefore, we conclude that the more fundamental tracer of galaxies' integrated dust temperatures are indeed their star-formation surface densities.