We report the investigation of temperature and excitation power dependence in photoluminescence spectroscopy measured in Mg-doped GaN epitaxial layers grown on sapphire by metalorganic chemical vapor deposition, The objective is to examine the effects of rapid-thermal annealing on Mg-related emissions. It is observed that the peak position of the 2.7-2.8 eV emission line is a function of the device temperature and annealing conditions, The phenomenon is attributed to Coulomb-potential fluctuations in the conduction and valence band edge and impurity levels due to the Mg-related complex dissociation. The blue shift of the 2.7-2.8 eV emission line with increasing excitation power provides clear evidence that a donor-acceptor recombination process underlies the observed emission spectrum. In addition, quenching of minor peaks at 3.2 and 3.3 eV are observed and their possible origin is discussed.