Pt/Co-based thin films of varying thicknesses were sputtered onto thermally oxidized Si substrates and capped with Cu, Au, or MgO layers. Vibrating sample magnetometry was employed to extract the magnetization at saturation () and the magnetic dead layer thickness () from the Co thickness dependence of the surface magnetic moment, following measurements at selected temperatures (, , and ) and cooling back to room temperature. By linear extrapolation of these data, and were determined for each temperature, enabling the analysis of their temperature dependence. The influence of the temperature on the perpendicular magnetic anisotropy (PMA), on the interfacial Dzyaloshinskii-Moriya interaction (DMI), and on the magnetic damping was investigated using a custom-built in situ system integrated into Brillouin light scattering and microstrip line ferromagnetic resonance (MS-FMR) setups. The damping constant showed a nonlinear dependence on the inverse effective thickness of the Co layer, attributed to a strong interfacial two-magnon scattering, particularly pronounced in Pt/Co/Au and Pt/Co/Cu structures. With increasing temperature, both the surface PMA and DMI constants decrease (in absolute value), although with a different dynamic of changes between different systems. This behavior is partly due to enhanced thermal fluctuations, which tend to reduce both DMI and anisotropy constants. Additionally, heating during measurements promotes interdiffusion and structural modifications, further influencing magnetic properties. In the case of Pt/Co/MgO, thermal treatment likely acts as an annealing process, enhancing both PMA and DMI by driving the demixing of oxygen atoms from the Co layer and promoting Co/O interface formation. This results in reduced temperature dependence of PMA and DMI for Pt/Co/MgO. Finally, clear correlations were observed between the surface PMA constant and and between the inhomogeneous FMR linewidth and the effective damping constant in the as-grown samples, which diminished with increasing measurement temperature.