This study investigated the variations in the permittivity with film thickness and measurement temperature of perfectly (111)-oriented Ba0.6Sr0.4TiO3 thin films with thicknesses ranging from 45 to 800 nm, which were prepared by RF magnetron sputtering on Pt/TiOx/SiO2/Si substrates. All the films showed elongations in the lattice parameter, suggesting the presence of residual strains but which were insensitive to the film thickness. The temperature-dependent measurement of the permittivity revealed an unusual Curie point independent of thickness, about 305 +/- 5 K, where the phase transition appeared frustrated. The thickness-dependent permittivity at a given temperature was explained by using the interfacial intrinsic low-permittivity layer model reported previously.