We examine by means of first-principles calculations the bcc-like (bcc: body centered cubic) to ω-like phase transformations in Ti-Al alloys with Nb additions at finite temperature. To simulate the alloy we use different discrete atomic configurations in a six atom unit cell of the stoichiometry Ti3Al2Nb. Calculated ground state energies show an instability in the ternary Ti3Al2Nb alloy against the ω structure type atomic displacement. To better understand the role of entropy in the stability/instability of these systems, the first-principles calculations are extended to finite temperature by including various contributions to the free energy. In particular, the vibrational free energy is calculated within a quasiharmonic approximation. It is shown that the bcc structure is stabilized by the contribution of the low energy modes to the lattice entropy against ω type atomic displacements. We find that configurational entropy plays a major role in the ω to B82 transformation. Calculated lattice parameters and transition temperatures are found to be in excellent agreement with experiment.