  We present a five-band Herschel study (100-500um) of three galaxy clusters at
z~1.2 from the Spitzer Adaptation of the Red-Sequence Cluster Survey (SpARCS).
With a sample of 120 spectroscopically-confirmed cluster members, we
investigate the role of environment on galaxy properties utilizing the
projected cluster phase space (line-of-sight velocity versus clustercentric
radius), which probes the time-averaged galaxy density to which a galaxy has
been exposed. We divide cluster galaxies into phase-space bins of (r/r200) x
(v/sigma_v), tracing a sequence of accretion histories in phase space. Stacking
optically star-forming cluster members on the Herschel maps, we measure average
infrared star formation rates, and, for the first time in high-redshift galaxy
clusters, dust temperatures for dynamically distinct galaxy
populations---namely, recent infalls and those that were accreted onto the
cluster at an earlier epoch. Proceeding from the infalling to virialized
(central) regions of phase space, we find a steady decrease in the specific
star formation rate and increase in the stellar age of star-forming cluster
galaxies. We perform a probability analysis to investigate all acceptable
infrared spectral energy distributions within the full parameter space and
measure a ~4 sigma drop in the average dust temperature of cluster galaxies in
an intermediate phase-space bin, compared to an otherwise flat trend with phase
space. We suggest one plausible quenching mechanism which may be consistent
with these trends, invoking ram-pressure stripping of the warmer dust for
galaxies within this intermediate accretion phase.
