  We demonstrate the usability of mm-wavelength imaging data obtained from the
APEX-SZ bolometer array to derive the radial temperature profile of the hot
intra-cluster gas out to radius r_500 and beyond. The goal is to study the
physical properties of the intra-cluster gas by using a non-parametric
de-projection method that is, aside from the assumption of spherical symmetry,
free from modeling bias. We use publicly available X-ray imaging data from the
XMM-Newton observatory and our Sunyaev-Zel'dovich Effect (SZE) imaging data
from the APEX-SZ experiment at 150 GHz to de-project the density and
temperature profiles for the relaxed cluster Abell 2204. We derive the gas
density, temperature and entropy profiles assuming spherical symmetry, and
obtain the total mass profile under the assumption of hydrostatic equilibrium.
For comparison with X-ray spectroscopic temperature models, a re-analysis of
the recent Chandra observation is done with the latest calibration updates.
Using the non-parametric modeling we demonstrate a decrease of gas temperature
in the cluster outskirts, and also measure the gas entropy profile. These
results are obtained for the first time independently of X-ray spectroscopy,
using SZE and X-ray imaging data. The contribution of the SZE systematic
uncertainties in measuring T_e at large radii is shown to be small compared to
the Chandra systematic spectroscopic errors. The upper limit on M_200 derived
from the non-parametric method is consistent with the NFW model prediction from
weak lensing analysis.
