  We present a detailed investigation of issues related to the measurement of
peculiar velocities and temperatures using Sunyaev-Zel'dovich (SZ) effects. We
estimate the accuracy to which peculiar velocities and gas temperatures of
distant galaxy clusters could be measured. With uK sensitivity on arcminute
scales at several frequencies it will be possible to measure peculiar
velocities to an accuracy of about 130 km/s and gas temperatures to better than
1 keV. The limiting factor for the accuracy of the measured peculiar velocity
is the presence of bulk motions within the galaxy cluster, even for apparently
relaxed clusters. The accuracy of the temperature is mainly limited by noise.
These results are independent of redshift. Such constraints can best be
achieved with only three frequencies: one in the Rayleigh-Jeans region (<40
GHz), one near 150 GHz, and the third at 300 GHz or higher. Measurements at the
null of the thermal SZ effect are of marginal utility, other than as a
foreground/background monitor.
