  One of the most promising solutions for the cooling flow problem involves
energy injection from the central AGN. However it is still not clear how
collimated jets can heat the ICM at large scale, and very little is known
concerning the effect of radio lobe expansion as they enter into pressure
equilibrium with the surrounding cluster gas. Cygnus A is one of the best
examples of a nearby powerful radio galaxy for which the synchrotron emitting
plasma and thermal emitting intra-cluster medium can be mapped in fine detail,
and previous observations have inferred possible shock structure at the
location of the cocoon. We use new XMM-Newton observations of Cygnus A, in
combination with deep Chandra observations, to measure the temperature of the
intra-cluster medium around the expanding radio cavities. We investigate how
inflation of the cavities may relate to shock heating of the intra-cluster gas,
and whether such a mechanism is sufficient to provide enough energy to offset
cooling to the extent observed.
