The crossover from an exciton gas to an electron-hole plasma is studied in a GaN/(Al,Ga)N single quantum well by means of combined time-resolved and continuous-wave photoluminescence measurements. The two-dimensional Mott transition is found to be of continuous type and to be accompanied by a characteristic modification of the quantum well emission spectrum. Beyond the critical density, the latter is strongly influenced by band-gap renormalization and Fermi filling of continuum states. Owing to the large binding energy of excitons in III-nitride heterostructures, their injection-induced dissociation could be tracked over a wide range of temperatures, i.e., from 4 to 150K. Various criteria defining the Mott transition are examined, which, however, do not lead to any clear trend with rising temperature: the critical carrier density remains invariant around 1012cm−2.