are much more sensitive to the combination of temperature and density than those at longer submillimeter/millimeter wavelengths, which primarily only trace the dust column density. In the Rayleigh-Jeans limit, the emission depends linearly on the dust temperature, but once this limit is violated the emission decreases exponentially with decreasing dust temperature. At 850 [$\mu$m]{}, the Rayleigh-Jeans limit is satisfied for $T >> 17$ K, but at 350 [$\mu$m]{}, this limit is only satisfied for $T >> 41$ K. Shirley et al. (2002) found a characteristic dust temperature for low-mass cores of $13.8 \pm 2.4$ K based on radiative transfer models of low-mass Class 0 protostars. Thus, observations at 850 [$\mu$m]{} are marginally within the Rayleigh-Jeans limit, but observations at 350 [$\mu$m]{} are not. The dust temperature of low-mass protostellar cores decreases from $\sim$ $50-300$ K in the inner regions of the cores[^9] to $\sim$ $7-10$ K in the intermediate regions far away from the central source but not directly exposed to the Interstellar Radiation Field (e.g., Evans et al. 2001; Shirley et al. 2002; Young et al. 2003). The 350 [$\mu$m]{} emission from these cores should thus decrease exponentially with increasing radius, meaning that the emission at this wavelength might 