The phonon–glass electron crystal concept is one of the key guiding principles for the development of efficient thermoelectric materials. Here, we confirm that SrTiO3 becomes a phonon–glass for large numbers of A-site vacancies in the Sr1–xLa0.67x□0.33xTiO3 series and show that its electron crystal properties are stymied by the presence of a core–shell grain structure. Thermal conductivity, heat capacity, and neutron powder diffraction, complemented by representational analysis and phonon calculations, were used to investigate the thermal transport. This reveals that the heat carrying modes are dominated by Sr motions and that these become more localized upon the introduction of the A-site vacancies, consistent with the observed phonon–glass state. Impedance spectroscopy and direct current electrical measurements were used to probe the electrical properties of insulating and conducting samples. This reveals the coring of grains due to oxidation on cooling from sintering temperatures. The resultant insulating shell limits the thermoelectric power factor to S2/ρ = 0.45 mW m–1 K–2 and the figure-of merit to ZT = 0.15 at 900 K for Sr0.20La0.53□0.27Ti0.95Nb0.05O3−δ. The thermal properties of these materials are, therefore, controlled by an intrinsic feature of the microstructure (i.e., the A-site vacancies), whereas the electrical properties are grain boundary limited, which in principle can be controlled independently to raise S2/ρ and ZT.