We have studied luminescence properties of Mg-doped GaN grown by hydride vapor phase epitaxy. Steady state photoluminescence (PL) spectra have been analyzed. Exciton, ultraviolet luminescence (UVL) and blue luminescence (BL) bands are the dominant PL bands in the spectra. At low temperature, Exciton and UVL bands show almost no shift with excitation intensity, whereas the BL band blueshifts by almost 0.4 𝑒𝑉 with increasing excitation intensity by seven orders of magnitude. Such shifting nature of bands with excitation intensity is explained by assuming that the BL band is detected from the region of the sample where potential fluctuations are very large, but the UVL and exciton bands originate from the region of the sample where there are no potential fluctuations. After the careful analysis of potential fluctuations model and the donor-acceptor pair model, we conclude that the BL band in the studied GaN:Mg sample is not a separate band but the UVL band itself, which is significantly distorted by potential fluctuations. Now, we call this band the BL* band. Temperature dependence of the BL*, UVL and Exciton peak intensity is analyzed. We see abrupt and tunable thermal quenching of the BL* and Exciton bands. Temperature dependence of the BL* and UVL bands at fixed excitation intensities but at different environmental conditions is also investigated. Finally, giant redshift of the BL* band with increasing temperature is explained by a combination of potential fluctuations and abrupt quenching of the BL* band with temperature.