Heavily doped single crystals of Gd3GaxAl5-xO12:Ce, Mg (x = 2.46–2.95) with different concentrations of Ce (0.016–0.188 at.%) and Mg (0–0.083 at.%) are investigated by the X-ray diffraction, photoluminescence, and thermoluminescence methods. Dependences of the luminescence characteristics, as well as crystal lattice parameters and distances between the Ce3+ and Mg2+ ions, on the Ga, Ce, and Mg concentration are studied. Mechanisms of the processes, resulting in the photoluminescence optical and thermal quenching and acceleration of decay kinetics, and the influence of the crystal composition on these processes are discussed. The role of close {Ce3+ - Mg2+Ga} pairs in these processes is considered. At T > 400 K, the luminescence thermal quenching is caused by the crossover process, while in the 200–350 K temperature range, by the electron transfer from the 5d1 excited state of Ce3+ to nearby defect levels (electron traps) located between the 5d1 level and the conduction band. The latter process results also in the appearance of thermally stimulated luminescence, and its efficiency depends on the Ga3+ content and concentration of intrinsic defects. The optimum concentrations of Ga3+ and Mg2+ ions in the investigated crystals are determined.