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 Γ ∼ 2.0 ± 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 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 ∼ 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 ∼ 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, cannot 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 β parameter around the volume-averaged equilibrium condition β ∼ 1.