The spectral energy distributions (SEDs) of dust-enshrouded galaxies with powerful restframe far-infrared emission have been constrained by a range of ground-based and space-borne surveys. The IRAS catalog provides a reasonably complete picture of the dust emission from nearby galaxies (at redshifts of order 0.1) that are typically less luminous than about 10 to the 12 solar luminosities. However, at higher redshifts, the observational coverage from all existing far-IR and submillimeter surveys is much less complete. Here we investigate the SEDs of a new sample of high-redshift submillimeter-selected galaxies (SMGs), for which redshifts are known, allowing us to estimate reliable luminosities and characteristic dust temperatures. We demonstrate that a wide range of SEDs is present in the population, and that a substantial number of luminous dusty galaxies with hotter dust temperatures could exist at similar redshifts (of order 2 to 3), but remain undetected in existing submillimeter surveys. These hotter galaxies could be responsible for about a third of the extragalactic IR background radiation at a wavelength of about 100 microns. The brightest of these galaxies would have far-IR luminosities of order 10 to the 13 solar luminosities and dust temperatures of order 60 K. Galaxies up to an order of magnitude less luminous with similar SEDs will be easy to detect and identify in the deepest Spitzer Space Telescope observations of extragalactic fields at 24 microns.