Photoluminescence (PL) spectra of GaAs quantum wells embedded in short-period AlAs/GaAs superlattices have been measured at 2 K and at room temperature. Two approaches have been applied in order to investigate the mechanisms of radiative recombination in these structures. In the first one, we studied the excitation density dependence of the PL intensity. In the second approach a line-shape analysis of the PL spectra is performed by means of a statistical model, which includes both free exciton, and free carrier recombinations. The fit based on this model reproduces with high accuracy the experimental spectra and allows to assess the relative contributions of excitons and free carriers to the radiative recombination process. The results of both approaches indicate the predominance of free excitons in the radiative recombination at room temperature.