Based on first-principle molecular dynamic simulations, we calculate the far-infrared spectra of small water clusters (H₂O)_n (n=2,4,6) at frequencies below 1000 cm^-1 and at 80 K and at atmospheric temperature (T > 200 K). We find that cluster size and temperature affect the spectra significantly. The effect of the cluster size is similar to the one reported for confined water. Temperature changes not only the shape of the spectra but also the total strength of the absorption, a consequence of the complete anharmonic nature of the classical dynamics at high temperature. In particular, we find that in the frequency region up to 320 cm^-1, the absorption strength per molecule of the water dimer at 220 K is significantly larger than that of bulk liquid water, while tetramer and hexamer show bulklike strengths. However, the absorption strength of the dimer throughout the far-infrared region is too small to explain the measured vapor absorption continuum, which must therefore be dominated by other mechanisms.