  We investigate the non-gravitational heating of hot gas in clusters of
galaxies (intracluster medium; ICM) on the assumption that the gas is heated
well before cluster formation ('preheating'). We examine the jet activities of
radio galaxies as the sources of excess energy in ICM, and the deformation of
the cosmic microwave background (the Sunyaev-Zel'dovich effect) by hot
electrons produced at the jet terminal shocks. We show that the observed excess
entropy of ICM and {\sl COBE/FIRAS} upper limit for the Compton $y$-parameter
are compatible with each other only when the heating by the jets occurred at
relatively small redshift ($z\lesssim 3$). Since this result contradicts the
assumption of 'preheating', it suggests that the heating occurred
simultaneously with or after cluster formation.
