We use new and archival Chandra observations of Cygnus A, totalling $sim$1.9 Ms, to investigate the distribution and temperature structure of gas lying within the projected extent of the cocoon shock and exhibiting a rib-like structure. We confirm that the X-rays are dominated by thermal emission with an average temperature of around 4 keV, and have discovered an asymmetry in the temperature gradient, with the southwestern part of the gas cooler than the rest by up to 2 keV. Pressure estimates suggest that the gas is a coherent structure of single origin located inside the cocoon, with a mass of roughly $2times10^{10} M_{odot}$. We conclude that the gas is debris resulting from disintegration of the cool core of the Cygnus A cluster after the passage of the jet during the early stages of the current epoch of activity. The 4 keV gas now lies on the central inside surface of the hotter cocoon rim. The temperature gradient could result from an offset between the centre of the cluster core and the Cygnus A host galaxy at the switch-on of current radio activity.
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