  The relativistic Sunyaev-Zel'dovich (SZ) effect offers a method, independent
of X-ray, for measuring the temperature of the intracluster medium (ICM) in the
hottest systems. Here, using N-body/hydrodynamic simulations of three galaxy
clusters, we compare the two quantities for a non-radiative ICM, and for one
that is subject both to radiative cooling and strong energy feedback from
galaxies. Our study has yielded two interesting results. Firstly, in all cases,
the SZ temperature is hotter than the X-ray temperature and is within ten per
cent of the virial temperature of the cluster. Secondly, the mean SZ
temperature is less affected by cooling and feedback than the X-ray
temperature. Both these results can be explained by the SZ temperature being
less sensitive to the distribution of cool gas associated with cluster
substructure. A comparison of the SZ and X-ray temperatures (measured for a
sample of hot clusters) would therefore yield interesting constraints on the
thermodynamic structure of the intracluster gas.
