We investigate the expected submillimeter emission and dust properties of the Lyman break galaxies (LBGs) in the Hubble Deep Field. The SCUBA Deep Survey (Hughes et al.) provides an upper limit of the 850 μm flux densities of the LBGs. With this constraint, we argue that a typical ultraviolet-to-far-infrared spectral shape of the high-redshift LBGs is rather close to a template spectrum of low-reddening starburst galaxies in the local universe but different from that of heavily dust-enshrouded ultraluminous far-infrared (FIR) galaxies like Arp 220. We also evaluate the lower limit temperature of dust in LBGs assuming a single- and two-component-modified blackbody spectrum. To estimate the total amount of energy reemitted in the FIR wavelength, we take two different approaches: the method of model fitting to the UV spectra of LBGs and an empirical method that uses the relationship between the UV spectral shape and the UV/FIR flux ratio observed for local starburst galaxies. Both methods give a lower limit temperature of ~40 K for the LBGs, which is higher than the typical dust temperature of local optical- and infrared-selected galaxies. This result is also supported by the comparison of the expected submillimeter flux of the LBGs with the cosmic FIR background radiation. The high dust temperature may indicate the effective massive star formation or the different dust properties in the high-redshift LBGs.