  We present far-infrared (FIR) analysis of 68 Brightest Cluster Galaxies
(BCGs) at 0.08 < z < 1.0. Deriving total infrared luminosities directly from
Spitzer and Herschel photometry spanning the peak of the dust component
(24-500um), we calculate the obscured star formation rate (SFR). 22(+6.2,-5.3)%
of the BCGs are detected in the far-infrared, with SFR= 1-150 M_sun/yr. The
infrared luminosity is highly correlated with cluster X-ray gas cooling times
for cool-core clusters (gas cooling time <1 Gyr), strongly suggesting that the
star formation in these BCGs is influenced by the cluster-scale cooling
process. The occurrence of the molecular gas tracing Ha emission is also
correlated with obscured star formation. For all but the most luminous BCGs
(L_TIR > 2x10^11 L_sun), only a small (<0.4 mag) reddening correction is
required for SFR(Ha) to agree with SFR_FIR. The relatively low Ha extinction
(dust obscuration), compared to values reported for the general star-forming
population, lends further weight to an alternate (external) origin for the cold
gas. Finally, we use a stacking analysis of non-cool-core clusters to show that
the majority of the fuel for star formation in the FIR-bright BCGs is unlikely
to originate form normal stellar mass loss.
