We present 107 maps of continuum emission at 350 microns from Galactic molecular clumps. Observed sources were mainly selected from the Bolocam Galactic Plane Survey (BGPS) catalog, with 3 additional maps covering star forming regions in the outer Galaxy. The higher resolution of the SHARC-II images (8.5 beam) compared with the 1.1 mm images from BGPS (33 beam) allowed us to identify a large population of smaller substructures within the clumps. A catalog is presented for the 1386 sources extracted from the 350 micron maps. The color temperature distribution of clumps based on the two wavelengths has a median of 13.3 K and mean of 16.3 +- 0.4 K, assuming an opacity law index of 1.7. For the structures with good determination of color temperatures, the mean ratio of gas temperature, determined from NH3 observations, to dust color temperature is 0.88 and the median ratio is 0.76. About half the clumps have more than two substructures and 22 clumps have more than 10. The fraction of the mass in dense substructures seen at 350 microns compared to the mass of their parental clump is ~0.19, and the surface densities of these substructures are, on average, 2.2 times those seen in the clumps identified at 1.1 mm. For a well-characterized sample, 88 structures (31%) exceed a surface density of 0.2 g cm^(-2), and 18 (6%) exceed 1.0 g cm^(-2), thresholds for massive star formation suggested by theorists.
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