Massive Population II galaxies undergoing the first phase of vigorous star formation after the initial Population III stage should have high energy densities and silicate-rich interstellar dust. We have modeled the resulting far-infrared spectral energy distributions (SEDs), demonstrating that they are shifted substantially to bluer ("warmer") wavelengths relative to the best fitting ones at z~3, and with strong outputs in the 10-40{mu}m range. When combined with a low level of emission by carbon dust, their SEDs match that of Haro 11, a local moderately low-metallicity galaxy undergoing a very young and vigorous starburst that is likely to approximate the relevant conditions in young Population II galaxies. We expect to see similar SEDs at high redshifts (z>~5) given the youth of galaxies at this epoch. In fact, we find a progression with redshift in observed galaxy SEDs, from those resembling local ones at 2<~z<4 to a closer resemblance with Haro 11 at 5<~z<7. In addition to the insight on conditions in high-redshift galaxies, this result implies that estimates of the total infrared luminosities at z~6 based on measurements near {lambda}~1mm can vary by factors of 2-4, depending on the SED template used. Currently popular modified blackbodies or local templates can result in significant underestimates compared with the preferred template based on the SED of Haro 11.