A detailed experimental investigation of the phonon-assisted emission in a high-quality c-plane GaN epilayer is presented up to 200 K. By performing photoluminescence and reflectivity measurements, we find important etaloning effects in the phonon-replica spectra, which have to be corrected before addressing the lineshape analysis. Direct experimental evidence for free exciton thermalization is found for the whole temperature range investigated. A close comparison with existing models for phonon replicas originating from a thermalized free exciton distribution shows that the simplified and commonly adopted description of the exciton-phonon interaction with a single excitonic band leads to a large discrepancy with experimental data. Only the consideration of the complex nature of the excitonic band in GaN, including A and B exciton contributions, allows accounting for the temperature dependence of the peak energy, intensity, and lineshape of the phonon replicas.