Thermally detected optical absorption (TDOA) and photoluminescence experiments are carried out on In0.16Ga0.84N/GaN multi-quantum wells (MQWs) grown by molecular beam epitaxy on (0001) sapphire substrates. A model proposed to adjust the TDOA line shape, allows to deduce the band-edge energies, the absorption coefficients and the broadening parameters of the (In,Ga)N MQWs for different thicknesses. The Fabry-Perot oscillations, which structure the TDOA spectra, are considered in this modelling to accurately account for the experimental data. The emission, which covers the whole visible spectrum at room temperature, is achieved by varying the thickness from 1.5 to 5 nm. A very large Stokes shift between the emission and absorption energies is deduced at low temperature, for the (In,Ga)N MQWs.