In photovoltaic devices, thermalization of hot carriers generated by high energy photons is one of the major loss mechanisms, which limits the power conversion efficiency of solar cells. Hot carrier solar cells are proposed to increase the efficiency of this technology by suppressing phonon-mediated thermalization channels and extracting hot carriers isentropically. Therefore, designing hot carrier absorbers, which can inhibit electron-phonon interactions and provide conditions for the re-absorption of the energy of non-equilibrium phonons by (hot) carriers, is of significant importance in such devices. As a result, it is essential to understand hot carrier relaxation mechanisms via phonon-mediated pathways in the system. In this work, the properties of photo-generated hot carriers in an InGaAs multi-quantum well structure are studied via steady-state photoluminescence spectroscopy at various lattice temperatures and excitation powers. It is observed that by considering the contribution of thermalized power above the absorber band edge, it is possible to evaluate hot carrier thermalization mechanisms via determining the thermalization coefficient of the sample. It is seen that at lower lattice temperatures, the temperature difference between hot carriers and the lattice reduces, which is consistent with the increase of the quasi-Fermi level splitting for a given thermalized power at lower lattice temperatures. Finally, the spectral linewidth broadening of multiple optical transitions in the QW structure as a function of the thermalized power is investigated.