Using density functional calculations the phonon dispersion relations, phonon density of states, and free energy of theta and alpha phases of alumina are investigated. The temperature dependence of the free energy indicates that entropy contributes to the destabilization of the alpha phase at the high temperatures, but this is insufficient to drive transformations between those two phases. The fcc arrangement of the oxygen sublattice plays an important role in the stabilization of the theta phase above 600 K. The present calculations explain the common presence of tetrahedrally coordinated Al cations in alumina, and suggest that some other than entropic mechanism exists, which stabilizes transition aluminas up to 1400 K. The present calculations go beyond the ground state energy calculations [C. Wolverton and K.C. Hass, Phys. Rev. B 63, 24102 (2001)], and give an additional understanding of the stability of transition alumina at finite temperatures.