The research demonstrates that nanostructuring the perovskite oxide SrTiO3 via 3D assemblage of nanocubes leads to a lower the thermal conductivity over a broad range of temperatures. This is particularly valuable in thermoelectric materials applications. The assemblages are comprised of pristine perovskite grain interiors confined by SrO or TiO2-rich interfaces resembling Ruddlesden Popper and Magneli phases.  The research also demonstrates that it is possible to generate vibrational fingerprints of the by a combination of lattice and molecular dynamics. TiO2-rich assemblages display splitting of the active modes similar to anatase providing a way to distinguish them from SrO-rich assemblages. Finally, we show that the IR active low vibrational frequencies are sensitive to the structure and could provide an efficient experimental route for identifying and characterizing materials with very low thermal conductivity.  The results are in the paper, while the repository contains the structures of all of the related structures used in the lattice and molecular dynamics calculations.