We analyze the room temperature photoluminescence properties of several multilayer stackings of GaN/AlN quantum dots. We report drastic differences of emission energies and linewidths between continuous wave and time-resolvedphotoluminescence experiments. In continuous wave experiments, the screening of internal electric fields by accumulation of e-h pairs in quantum dot planes induces a blue-shift as well as an unexpected narrowing of the emission line, when the laser intensity is increased. Under intense, pulsed excitation, in time-resolvedphotoluminescence, a substantial blue-shift is induced, due to the partial cancelation of the quantum confined Stark effect. When the system is again free to relax, we observe a time-dependent red-shift of the line, which maintains a fairly constant width. We attribute the observed behavior of energies and linewidths to the intricate contributions of the in-plane distribution of dot sizes and of the depth-dependent decrease of the degree of excitation of the different planes. We support our interpretations by the use of a model based on a self-consistent solution of the Schrödinger and Poisson equations within the envelope function approximation.