  Two lines of evidence indicate that active galaxies, principally radio
galaxies, have heated the diffuse hot gas in clusters. The first is the general
need for additional heating to explain the steepness of the X-ray
luminosity--temperature relation in clusters, the second is to solve the
cooling flow problem in cluster cores. The inner core of many clusters is
radiating energy as X-rays on a timescale much shorter than its likely age.
Although the temperature in this region drops by a factor of about 3 from that
of the surrounding gas, little evidence is found for gas much cooler than that.
Some form of heating appears to be taking place, probably by energy transported
outward from the central accreting black hole or radio source. How that energy
heats the gas depends on poorly understood transport properties (conductivity
and viscosity) of the intracluster medium. Viscous heating is discussed as a
possibility. Such heating processes have consequences for the truncation of the
luminosity function of massive galaxies.
