We construct a SCUBA-2 450 μm map in the COSMOS field that covers an area of 300 arcmin2 and reaches a 1σ noise level of 0.65 mJy in the deepest region. We extract 256 sources detected at 450 μm with signal-to-noise ratios >4.0 and analyze the physical properties of their multiwavelength counterparts. We find that most of the sources are at z ≲ 3, with a median of $z={1.79}_{-0.15}^{+0.03} \% $ . About ${35}_{-25}^{+32} \% $ of our sources are classified as starburst galaxies based on their total star formation rates (SFRs) and stellar masses (M*). By fitting the far-infrared spectral energy distributions, we find that our 450 μm selected sample has a wide range of dust temperatures (20 K ≲ Td ≲ 60 K), with a median of ${T}_{{\rm{d}}}={38.3}_{-0.9}^{+0.4}$ K. We do not find a redshift evolution in dust temperature for sources with ${L}_{\mathrm{IR}}\gt {10}^{12}\,{L}_{\odot }$ at z < 3. However, we find a moderate correlation where the dust temperature increases with the deviation from the SFR─M* relation. The increase in dust temperature also correlates with optical morphology, which is consistent with merger-triggered starbursts in submillimeter galaxies. Our galaxies do not show the tight IRX─βUV correlation that has been observed in the local universe. We construct the infrared luminosity functions of our 450 μm sources and measure their comoving SFR densities (SFRDs). The contribution of the ${L}_{\mathrm{IR}}\gt {10}^{12}\,{L}_{\odot }$ population to the SFRD rises dramatically from z = 0 to 2 (∝(1 + z)3.9±1.1) and dominates the total SFRD at z ≳ 2.