We present the results of an X-ray analysis of 80 galaxy clusters selected in the 2500 deg2 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 a joint X-ray spectral 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 < 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 < 1.2) clusters are slightly (∼30%) cooler both in the inner (r < 0.1R500) and outer (r>R500) regions
than their low-z (0.3 < 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.
Confirming earlier results from this data set, we find an absence of strong cool cores at high z, manifested in
this analysis as a significantly lower observed pressure in the central 0.1R500 of the high-z cool-core subset of
clusters compared to the low-z cool-core subset. 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—this may reflect a long-standing
balance between cooling and feedback over long timescales and large physical scales. 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 (∼3×) 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.