We discuss a new method of finding the cluster temperatures which is independent of distance and therefore very useful for distant clusters. The hot gas of electrons in clusters of galaxies scatters and distorts the cosmic microwave background radiation in a well determined way. This Sunyaev-Zel'dovich (SZ) effect is a useful tool for extracting information about clusters such as their peculiar radial velocity and optical depth. Here we show how the temperature of the cluster can be inferred from the SZ effect, in principle without use of X-ray data. We use recent millimetre observation of Abell 2163 to determine for the first time a cluster temperature using SZ observations only. The result T_e = 26^+34_-19 keV at 68% confidence level (at 95% c.l. we find T>1.5 keV) is in reasonable agreement with the X-ray results, T_e =12.4^+2.8_-1.9 keV.