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We examine atmospheric heating by radio active galactic nuclei (AGN) indistant X-ray clusters by cross correlating clusters selected from the 400Square Degree (400SD) X-ray Cluster survey with radio sources in the NRAO VLASky Survey. Roughly 30% of the clusters show radio emission above a fluxthreshold of 3 mJy within a projected radius of 250 kpc. The radio emission ispresumably associated with the brightest cluster galaxy. The mechanical jetpower for each radio source was determined using scaling relations betweenradio power and cavity (mechanical) power determined for nearby clusters,groups, and galaxies with hot atmospheres containing X-ray cavities. Theaverage jet power of the central radio AGN is approximately $2\times10^{44}$\ergs. We find no significant correlation between radio power, hencemechanical jet power, and the X-ray luminosities of clusters in the redshiftrange 0.1 -- 0.6. This implies that the mechanical heating rate per particle ishigher in lower mass, lower X-ray luminosity clusters. The jet power averagedover the sample corresponds to an atmospheric heating of approximately 0.2 keVper particle within R$_{500}$. Assuming the current AGN heating rate does notevolve but remains constant to redshifts of 2, the heating rate per particlewould rise by a factor of two. We find that the energy injected from radio AGNcontribute substantially to the excess entropy in hot atmospheres needed tobreak self-similarity in cluster scaling relations. The detection frequency ofradio AGN is inconsistent with the presence of strong cooling flows in 400SDclusters, but does not exclude weak cooling flows. It is unclear whethercentral AGN in 400SD clusters are maintained by feedback at the base of acooling flow. Atmospheric heating by radio AGN may retard the development ofstrong cooling flows at early epochs.

Average Heating Rate of Hot Atmospheres in Distant Clusters by Radio AGN: Evidence for Continuous AGN Heating