Ionic displacements in ferroelectric BaTiO₃ lead to a broken inversion symmetry associated with the spontaneous polarization. Upon heating a strained BaTiO₃ thin film experiences a transition from the tetragonal to the quasi-cubic phase, which goes hand in hand with a strong reduction of the ferroelectric polarization and a sign reversal of the linear expansion coefficient from negative to positive (Choi et al.). According to time-dependent DFT calculations (Lian at al.), an above-bandgap optical excitation leads to an electron transfer from the occupied O2p to the unoccupied Ti3d orbitals, which reduces the polarization. In this study, we show that an above-bandgap optical pump triggers an heat-induced reversible structural phase transition and an electron- and structural- induced polarization change in the 100 fs to ps time scale. We employ time-resolved X-ray diffraction and time-resolved Second Harmonic Generation (SHG) to disentangle the dynamics in structure and polarization during the photo-induced structural phase transition of a BaTiO₃ ferroelectric thin film.