Understanding the damping mechanism in finite size systems and its dependence on temperature is a critical step in the development of magnetic nanotechnologies. In this work, nano-sized materials are modeled via atomistic spin dynamics, the damping parameter being extracted from Ferromagnetic Resonance (FMR) simulations applied for FePt systems, generally used for heat-assisted magnetic recording media (HAMR). We find that the damping increases rapidly close to T C and the effect is enhanced with decreasing system size, which is ascribed to scattering at the grain boundaries. Additionally, FMR methods provide the temperature dependence of both damping and the anisotropy, important for the development of HAMR. Semi-analytical calculations show that, in the presence of a grain size distribution, the FMR linewidth can decrease close to the Curie temperature due to a loss of inhomogeneous line broadening. Although FePt has been used in this study, the results presented in the current work are general and valid for any ferromagnetic material.