The electronic conductivity and the redox activity of metal oxides depend on the extent of the wave function spread of the electronic charge carriers. Delocalized (free) electrons and holes lead to large electronic conductivity, whereas self-trapped (small polaron) electrons and holes provide active centers for charge transfer and redox reactions. It is possible to control the state of the electronic charge carriers in metal oxides, free vs. self-trapped, by utilizing mechanical stress and strain. Tensile stresses tend to favor trapping, and the critical tensile stress above which trapping occurs also depends strongly on temperature. Here we adopt SrTiO₃ as a model system and computationally predict regimes of trapping or delocalization for electrons and holes as a function of hydrostatic stress and temperature. SrTiO₃ is a representative of the perovskite family of metal oxides, and itself is a widely used crystal for electronic studies. Starting from density functional theory (DFT), we parametrized on-site Hubbard terms (+U) for Ti 3d states and O 2p states that adhere to the generalized Koopman’s theorem. This adherence qualifies DFT equipped with the selected U to accurately describe trapped electrons and holes. Using this DFT+U approach we found that in SrTiO₃ at zero temperature and zero stress, trapped holes on oxygen ions are favored by 170 meV, whereas free electrons are favored by 110 meV.  Using the quasiharmonic approximation we extend these results to finite temperature and finite hydrostatic stress. In particular we calculate the Gibbs free energy of formation of electrons and holes in both trapped and free states. Based on these free energies, we build a stress-temperature diagram for the predominant electronic defect state. The analysis we present here for SrTiO₃ is broadly applicable to other semiconducting metal oxides, and illustrates how strain (or stress) can serve as a modulator of electronic charge carriers.