A challenge in the preparation of advanced materials that exist only as thin films is to establish their properties, particularly when the materials are of low symmetry or the tensor properties of interest are of high rank. Using Sr4Bi4Ti7O24 as an example, we show how the preparation of oriented epitaxial films of multiple orientations enables the thermal conductivity tensor of this tetragonal material with a c-axis length of 64.7 Å to be measured. The thermal conductivity tensor coefficients k33 = 1.10 W m−1 K−1 and k11 = k22 = 1.80 W m−1 K−1 were determined by growing epitaxial Sr4Bi4Ti7O24 films on (100), (110), and (111) SrTiO3 substrates.