Photoluminescence (PL) and reflectivity spectra of a high-quality InGaAs/GaAs quantum well structure reveal a series of ultra-narrow peaks attributed to the quantum confined exciton states. The intensity of these peaks decreases as a function of temperature, while the linewidths demonstrate a complex and peculiar behavior. At low pumping the widths of all peaks remain quite narrow (< 0.1 meV) in the whole temperature range studied, 4 -30 K. At the stronger pumping, the linewidth first increases and than drops down with the temperature rise. Pump-probe experiments show two characteristic time scales in the exciton decay, < 10 ps and 15 -45 ns, respectively. We interpret all these data by an interplay between the exciton recombination within the light cone, the exciton relaxation from a nonradiative reservoir to the light cone, and the thermal dissociation of the nonradiative excitons. The broadening of the low energy exciton lines is governed by the radiative recombination and scattering with reservoir excitons while for the higher energy states the linewidths are also dependent on the acoustic phonon relaxation processes.