We report detections of six high-redshift (1.8 < z < 6.4), optically luminous, radio-quiet quasars at 350 micron, using the SHARC II bolometer camera at the Caltech Submillimeter Observatory. Our observations double the number of high-redshift quasars for which 350 micron photometry is available. By combining the 350 micron measurements with observations at other submillimeter/millimeter wavelengths, for each source we have determined the temperature of the emitting dust (ranging from 40 to 60 K) and the far-infrared luminosity (0.6 to 2.2 x 10(13) Lo). The combined mean spectral energy distribution (SED) of all high-redshift quasars with two or more rest frame far-infrared photometric measurements is best fit with a greybody with temperature of 47 +- 3 K and a dust emissivity power-law spectral index of beta = 1.6 +- 0.1. This warm dust component is a good tracer of the starburst activity of the quasar host galaxy. The ratio of the far-infrared to radio luminosities of infrared luminous, radio-quiet high-redshift quasars is consistent with that found for local star-forming galaxies.