Understanding the physical mechanisms behind thermal effects in phosphors is crucial for white light-emitting device (WLEDs) applications, as thermal quenching of their photoluminescence might render them useless. We analyze from first-principles, before and after absorption/emission of light, two chemically close Eu-doped Ba₃Si₆O₁₂N₂ and Ba₃Si₆O₉N₄ crystals for WLEDs. The first one has an almost constant emission intensity with increasing temperature whereas the other one does not. Our results, in which the Eu-5d levels are obtained inside the band gap thanks to the removal of an electron from the 4f⁷ shell, and the atomic neighborhood properly relaxed in the excited state, attributes the above-mentioned experimental difference to an autoionization model of the thermal quenching, based on the energy difference between Eu 5d and the conduction band minimum. Our depleted-shifted 4f method can identify luminescent centers and therefore allows for effective crystal site engineering of luminescent centers in phosphors from first principles.