Based on first-principle calculations, we have systematically explored the nature of the elastic stability and the delta-delta'-epsilon phase transitions in pure Pu at high temperature. It is found that, both the electronphonon coupling and the spin fluctuation effects tend to decrease the tetragonal elastic constant (C') of delta-Pu, accounting for its anomalous softening at high temperature. The lattice thermal expansion together with the electron-phonon coupling can stiffen C' of epsilon-Pu, promoting its mechanical stability at high temperature. The delta-epsilon transition is calculated to take place around 750-800 K, and is dominated by the phonon vibration. The delta' intermediate phase is realized around 750 K mainly because of the thermal spin fluctuation.
