We have studied the thermal quenching of the ultraviolet luminescence band with a maximum at about 3.25 eV in p-type Mg-doped GaN. The characteristic temperature of the thermal quenching of photoluminescence (PL) gradually shifted to higher temperatures with increasing excitation intensity. This effect is explained by a population inversion of charge carriers at low temperatures, which suddenly converts into a quasiequilibrium population as the temperature increases above the characteristic value. Tunable quenching of PL has been observed only in some of the GaN: Mg samples. The absence of the tunable quenching of PL in another group of GaN: Mg samples is preliminarily attributed to different types of dominant nonradiative defects in the two groups of samples.