  (Abridged) We present the results of an X-ray analysis of 80 galaxy clusters
selected in the 2500 deg^2 South Pole Telescope survey and observed with the
Chandra X-ray Observatory. We divide the full sample into subsamples of ~20
clusters based on redshift and central density, performing an X-ray fit to all
clusters in a subsample simultaneously, assuming self-similarity of the
temperature profile. This approach allows us to constrain the shape of the
temperature profile over 0<r<1.5R500, which would be impossible on a
per-cluster basis, since the observations of individual clusters have, on
average, 2000 X-ray counts. The results presented here represent the first
constraints on the evolution of the average temperature profile from z=0 to
z=1.2. We find that high-z (0.6<z<1.2) clusters are slightly (~40%) cooler both
in the inner (r<0.1R500) and outer (r>R500) regions than their low-z
(0.3<z<0.6) counterparts. Combining the average temperature profile with
measured gas density profiles from our earlier work, we infer the average
pressure and entropy profiles for each subsample. Overall, our observed
pressure profiles agree well with earlier lower-redshift measurements,
suggesting minimal redshift evolution in the pressure profile outside of the
core. We find no measurable redshift evolution in the entropy profile at
r<0.7R500. We observe a slight flattening of the entropy profile at r>R500 in
our high-z subsample. This flattening is consistent with a temperature bias due
to the enhanced (~3x) rate at which group-mass (~2 keV) halos, which would go
undetected at our survey depth, are accreting onto the cluster at z~1. This
work demonstrates a powerful method for inferring spatially-resolved cluster
properties in the case where individual cluster signal-to-noise is low, but the
number of observed clusters is high.
