An oxygen-defective perovskite oxide with the title composition has been prepared by soft-chemistry procedures followed by quenching in liquid N(2) from 900 degrees C. This polycrystalline sample has been characterized by temperature-dependent X-ray (XRPD) and neutron powder diffraction (NPD), thermal analysis, electrical conductivity and thermal expansion measurements, in order to correlate the physico-chemical properties and the structural features. At room temperature (RT), the sample adopts an orthorhombic brownmillerite-like structure defined in the Ibm2 space group, containing layers of CoO(6) octahedra alternating with layers of CoO(4) tetrahedra along the b axis. This phase is stable between room temperature and 350 degrees C, where a topotactic intake of oxygen increases the coordination of the tetrahedra to octahedral, with change of the space group to Pnma, as unveiled by the in-situ NPD study. This intermediate phase has been identified for the first time. At 653 degrees C, this phase irreversibly transforms to a hexagonal "H" phase. At 920 degrees C, a cubic perovskite phase "C" is identified, which is transformed again, upon cooling, into the "H" phase at 774 degrees C. The features of the very distinct coordination polyhedra present in the different polymorphs have been correlated with the transport properties. There is a substantial increment of the conductivity at 350 degrees C, upon the oxygen insertion process, concomitant with a contraction of the axial Co-O bonds of the octahedral CoO(6) units and the transformation of the tetrahedra into octahedra, also characterized by dilatometry measurements. The dramatic reduction of the conductivity above 700 degrees C is connected with the transformation to the "H" polymorph, with a complete oxygen sublattice and a face-sharing octahedral framework with a poor 1D electronic conduction. In Sr(0.8)Ba(0.2)CoO(2.5), the plateau of stability of the 3C-like structure, with useful transport properties in the range of sigma = 50-60 S cm(-1), is extended up to 650 degrees C with respect to the pristine SrCoO(2.5). By heating above 900 degrees C, the conductivity abruptly rises when the sample is entering the cubic perovskite region, characterized by a three-dimensional vertex-sharing network of CoO(6) octahedra. The total conductivity displays a maximum value of 75 S cm(-1) at 900 degrees C, which increases during the cooling run, exhibiting a typical metallic behaviour. Moreover, in this cubic phase, the oxygen atoms show large thermal factors of 5.5 A(2), suggesting a considerable mobility and a mixed conductor behaviour.