Phonon vibrations strongly affect the terahertz responses of condensed matter, which lies at the cutting-edge technological strategies for not only telecommunication but also information read/write. The finite temperature of phonon vibration, however, is a higher order interaction that incorporates multiple phonon couplings. This is not straightforwardly calculated, and has rarely been studied in previous works. We illustrate the thermal effect on terahertz responses using the well-known perovskite oxides, BaTiO₃ and PbTiO₃. It could provide experimentally observable phonon dispersions that are stable in all temperature regime. In addition, we suggest that intermediate terahertz laser would trigger phase transitions in both of these systems, showing evidence to induce hidden phases that does not appear in the conventional P-T phase diagram. Nambu-Goldstone and Higgs modes in Mexican-hat energy landscape are also explored. Our work has just appeared in Physical Review Applied, at https://link.aps.org/doi/10.1103/PhysRevApplied.20.024020.