PbTiO 3 is a prototypical ferroelectric perovskite that is known to undergo a temperature driven ferroelectric tetragonal to paraelectric cubic phase transition, but the understanding of some key phenomena and associated mechanisms underlying this transition remains unclear. Here, using molecular dynamics simulations based on first-principles effective Hamiltonian, we show the behaviors of the phase transition temperature Tc and adiabatic temperature change ΔT of PbTiO3 under an external electric field and tensile stress along the [001] direction. Our results show that the electric field E induces rising Tc via a linear relationTc∝ 0.3083E, rendering the phase transition to go from first-order with thermal hysteresis to second-order without thermal hysteresis above ∼200 kV/cm; meanwhile, a maximum electrocaloric response ΔTmax∼34 K is obtained under E=500 kV/cm. Moreover, external stress (σz) causes rising Tc via a linear relationTc∝160σz and improves the electrocaloric response ΔTmax when combined with the electric field. The present results offer insights into the physical processes and mechanisms that dictate finite-temperature properties of ferroelectric perovskite oxides, laying a foundation for further exploration of this intriguing class of materials.