We present the first comprehensive comparison between free energies, based on a phonon dispersion calculation within density functional theory, of theoretically predicted structures and the experimentally proposed a (P6(1)) and beta (Fddd) phases of the promising hydrogen storage material Mg(BH4)(2). The recently proposed low-density I (4) over bar m2 ground state is found to be thermodynamically unstable, with soft acoustic phonon modes at the Brillouin zone boundary. We show that such acoustic instabilities can be detected by a macroscopic distortion of the unit cell. Following the atomic displacements of the unstable modes, we have obtained a new F222 structure, which has a lower energy than all previously experimentally and theoretically proposed phases of Mg( BH4) 2 and is free of imaginary eigenmodes. A new meta-stable high-density I4(1)/amd structure is also derived from the I (4) over bar m2 phase. Temperatures for the decomposition are found to be in the range of 400-470 K and largely independent of the structural complexity, as long as the primary cation coordination polyhedra are properly represented. This opens a possibility of using simple model structures for screening and prediction of finite temperature stability and decomposition temperatures of novel borohydride systems.