  The fluctuations in the Cosmic Microwave Background (CMB) intensity due to
the Sunyaev-Zeldovich (SZ) effect are the sum of a thermal and a kinetic
contribution. Separating the two components to measure the peculiar velocity of
galaxy clusters requires radio and microwave observations at three or more
frequencies, and knowledge of the temperature T_e of the intracluster medium
weighted by the electron number density. To quantify the systematics of this
procedure, we extract a sample of 117 massive clusters at redshift z=0 from an
N-body hydrodynamical simulation, with 2x480^3 particles, of a cosmological
volume 192 Mpc/h on a side of a flat Cold Dark Matter model with Omega_0=0.3
and Lambda=0.7. Our simulation includes radiative cooling, star formation and
the effect of feedback and galactic winds from supernovae. We find that (1) our
simulated clusters reproduce the observed scaling relations between X-ray and
SZ properties; (2) bulk flows internal to the intracluster medium affect the
velocity estimate by less than 200 km/s in 93 per cent of the cases; (3) using
the X-ray emission weighted temperature, as an estimate of T_e, can
overestimate the peculiar velocity by 20-50 per cent, if the microwave
observations do not spatially resolve the cluster. For spatially resolved
clusters, the assumptions on the spatial distribution of the ICM, required to
separate the two SZ components, still produce a velocity overestimate of 10-20
per cent, even with an unbiased measure of T_e. Thanks to the large size of our
cluster samples, these results set a robust lower limit of 200 km/s to the
systematic errors that will affect upcoming measures of cluster peculiar
velocities with the SZ effect.
