The thermal conductivity of a series of complex aluminates, RE(2)SrAl(2)O(7), with different rare-earth (RE) ions, has been measured up to 1000 degrees C. There is a strong dependence on the atomic number of the RE ion, ranging from an approximately 1/T dependence for the lanthanum strontium aluminate to an almost temperature-independent behavior of the dysprosium strontium aluminate. The latter conductivity is comparable with that of yttria-stabilized zirconia, the current material of choice for thermal barrier coatings. The temperature dependence of the thermal conductivities of all the aluminates studied can be fit to a standard phonon-phonon scattering model, modified to account for a minimum phonon mean free path, in which the difference in behavior is attributed to increased phonon-phonon scattering with the atomic mass of the RE ion. Although a satisfactory parametric fit is obtained, the model does not take into account either the detailed layer structure of the aluminates, consisting of alternating rock-salt and perovskite layers in a natural superlattice structure, or the site preferences of the RE ion. This suggests that further model development is warranted.