We present an ALMA-Herschel joint analysis of sources detected by the ALMA Lensing Cluster Survey (ALCS) at 1.15 mm. Herschel/PACS and SPIRE data at 100-500 mu m are deblended for 180 ALMA sources in 33 lensing cluster fields that are detected either securely (141 sources; in our main sample) or tentatively at S/N >= 4 with cross-matched HST/Spitzer counterparts, down to a delensed 1.15 mm flux density of similar to 0.02 mJy. We performed far-infrared spectral energy distribution modeling and derived the physical properties of dusty star formation for 125 sources (109 independently) that are detected at >2 sigma in at least one Herschel band. A total of 27 secure ALCS sources are not detected in any Herschel bands, including 17 optical/near-IR-dark sources that likely reside at z = 4.2 +/- 1.2. The 16th, 50th, and 84th percentiles of the redshift distribution are 1.15, 2.08, and 3.59, respectively, for ALCS sources in the main sample, suggesting an increasing fraction of z similar or equal to 1 - 2 galaxies among fainter millimeter sources (f(1150) similar to 0.1 mJy). With a median lensing magnification factor of mu = 2.6(-0.8)(+2.6), ALCS sources in the main sample exhibit a median intrinsic star formation rate of 94(-54)(+84) M-circle dot yr(-1), lower than that of conventional submillimeter galaxies at similar redshifts by a factor of similar to 3. Our study suggests weak or no redshift evolution of dust temperature with L-IR < 10(12) L-circle dot galaxies within our sample at z similar or equal to 0 - 2. At L-IR > 10(12) L-circle dot, the dust temperatures show no evolution across z similar or equal to 1-4 while being lower than those in the local universe. For the highest-redshift source in our sample (z = 6.07), we can rule out an extreme dust temperature (>80 K) that was reported for MACS0416 Y1 at z = 8.31.