The δ-AlOOH can transport water into the deep mantle along cold subducting slab geotherm. We investigate the hydrogen-bond symmetrization behavior of δ-AlOOH under the relevant pressure-temperature condition of the lower mantle using ab initio molecular dynamics (MD). The static symmetrization pressure of 30.0 GPa can be reduced to 17.0 GPa at 300 K by finite-temperature (T) statistics, closer to the experimental observation of ∼10.0 GPa. The symmetrization pressure obtained by MD simulation is related to T by P (GPa) + 13.9 (GPa) = 0.01 (GPa/K) × T (K). We conclude that δ-AlOOH in the lower mantle exists with symmetric hydrogen bond from its birthplace, or someplace slightly deeper, to the core-mantle boundary (CMB) along cold subducting slab geotherm. The bulk modulus decreases with T and increases anomalously upon symmetrization: for δ-AlOOH with asymmetric hydrogen bond, and for δ-AlOOH with symmetric hydrogen bond. Our results provide an important insight into the existent form and properties of δ-AlOOH in the lower mantle.