Brillouin light scattering and microstrip line ferromagnetic resonance were used to study perpendicular magnetic anisotropy (PMA), magnetic damping, and interfacial Dzyaloshinskii-Moriya interaction (iDMI) in $X$/Fe(${t}_{\mathrm{Fe}}$)/$Y$ thin films with varying Fe thickness $(1.4\phantom{\rule{0.16em}{0ex}}\mathrm{nm}\ensuremath{\le}{t}_{\mathrm{Fe}}\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$, where $X$ stands for Pt, Ir, or Cu and $Y$ stands for Ir, Cu, or MgO. A particular interest is given to their temperature dependence. To accurately assess the contribution of each interface with Fe to the effective interface PMA constant, we combined direct measurements of the effective magnetization thickness dependence with the spin waves frequency mismatch. Notably, Ir/Fe and Fe/Ir, as well as Cu/Fe and Fe/Cu interfaces exhibited distinct behaviors: Fe/Ir significantly contributed to PMA and spin pumping induced damping. The damping constant showed a nonlinear dependence on the Fe layer inverse effective thickness, which was linked to a strong interfacial two-magnon scattering, particularly evident in Cu/Fe/Ir and Cu/Fe/Cu structures. Additionally, iDMI measurements revealed an opposite chirality of Pt/Fe and Ir/Fe interfaces. We also investigated how these magnetic interfacial properties vary with temperature in the Pt/Fe/Cu and Cu/Fe/Cu systems. We found that the interface PMA constant increased linearly with temperature, while the iDMI constant decreased significantly, by approximately 60%. This suggests that iDMI is highly sensitive to thermal disorder. Post-temperature measurements indicated that the temperature induces interdiffusion and impacts the magnetic properties through specific effects that are challenging to disentangle in the absence of in situ magnetization measurements.