We report on Suzaku observations of selected regions within the Southern giant lobe of the radio galaxy Centaurus A . In our analysis we focus on distinct X-ray features detected with the X-ray Imaging Spectrometer within the range 0.5 - 10 keV , some of which are likely associated with fine structure of the lobe revealed by recent high-quality radio intensity and polarization maps . With the available photon statistics , we find that the spectral properties of the detected X-ray features are equally consistent with thermal emission from hot gas with temperatures kT > 1 keV , or with a power-law radiation continuum characterized by photon indices \Gamma \sim 2.0 \pm 0.5 . However , the plasma parameters implied by these different models favor a synchrotron origin for the analyzed X-ray spots , indicating that a very efficient acceleration of electrons up to \gtrsim 10 TeV energies is taking place within the giant structure of Centaurus A , albeit only in isolated and compact regions associated with extended and highly polarized radio filaments . We also present a detailed analysis of the diffuse X-ray emission filling the whole field-of-view of the instrument , resulting in a tentative detection of a soft excess component best fitted by a thermal model with a temperature of kT \sim 0.5 keV . The exact origin of the observed excess remains uncertain , although energetic considerations point to thermal gas filling the bulk of the volume of the lobe and mixed with the non-thermal plasma , rather than to the alternative scenario involving a condensation of the hot intergalactic medium around the edges of the expanding radio structure . If correct , this would be the first detection of the thermal content of the extended lobes of a radio galaxy in X-rays . The corresponding number density of the thermal gas in such a case is n _ { g } \sim 10 ^ { -4 } cm ^ { -3 } , while its pressure appears to be in almost exact equipartition with the volume-averaged non-thermal pressure provided by the radio-emitting electrons and the lobes ’ magnetic field . A prominent large-scale fluctuation of the Galactic foreground emission , resulting in excess foreground X-ray emission aligned with the lobe , can not be ruled out . Although tentative , our findings potentially imply that the structure of the extended lobes in active galaxies is likely to be highly inhomogeneous and non-uniform , with magnetic reconnection and turbulent acceleration processes continuously converting magnetic energy to internal energy of the plasma particles , leading to possibly significant spatial and temporal variations in the plasma \beta parameter around the volume-averaged equilibrium condition \beta \sim 1 .