We present a Faraday rotation measure ( RM ) study of the diffuse , polarized , radio emission from the giant lobes of the nearest radio galaxy , Centaurus A . After removal of the smooth Galactic foreground RM component , using an ensemble of background source RMs located outside the giant lobes , we are left with a residual RM signal associated with the giant lobes . We find the most likely origin of this residual RM is from thermal material mixed throughout the relativistic lobe plasma . The alternative possibility of a thin-skin/boundary layer of magnetoionic material swept up by the expansion of the lobes is highly unlikely since it requires , at least , an order of magnitude enhancement of the swept up gas over the expected intragroup density on these scales . Strong depolarisation observed from 2.3 to 0.96 GHz also supports the presence of a significant amount of thermal gas within the lobes ; although depolarisation solely due to RM fluctuations in a foreground Faraday screen on scales smaller than the beam can not be ruled out . Considering the internal Faraday rotation scenario , we find a thermal gas number density of \sim 10 ^ { -4 } cm ^ { -3 } implying a total gas mass of \sim 10 ^ { 10 } M _ { \odot } within the lobes . The thermal pressure associated with this gas ( with temperature kT \sim 0.5 keV , obtained from recent X-ray results ) is approximately equal to the non-thermal pressure , indicating that over the volume of the lobes , there is approximate equipartition between the thermal gas , radio-emitting electrons and magnetic field ( and potentially any relativistic protons present ) .