  Understanding the physical mechanisms behind thermal effects in phosphors is
crucial for white light-emitting diodes (WLEDs) applications, as thermal
quenching of their photoluminescence might render them useless. The two
chemically close Eu-doped \Hosta and \Hostb crystals are typical phosphors
studied for WLEDs. The first one sustains efficient light emission at
100$^{\circ}$C while the second one emits very little light at that
temperature. Herein, we analyze from first principles their electronic
structure and atomic geometry, before and after absorption/emission of light.
Our results, in which the Eu-5d levels are obtained inside the band gap thanks
to the removal of an electron from the 4f$^7$ shell, attributes the
above-mentioned experimental difference to an auto-ionization model of the
thermal quenching, based on the energy difference between Eu$_{\text{5d}}$ and
the conduction band minimum. For both Eu-doped phosphors, we identify the
luminescent center, and we show that the atomic relaxation in their excited
state is of crucial importance for a realistic description of the emission
characteristics.
