We employ an atomistic model using a nearest-neighbor Heisenberg Hamiltonian exchange to study computationally the dependence of the Curie temperature of L1 0 -FePt on finite-size and surface effects in heat-assisted magnetic recording (HAMR) media. We demonstrate the existence of a size threshold at 3.5 nm below which the impact of finite-size effects starts to permeate into the center of the grains and contributes to the reduction of the Curie temperature. We find a correlation between the Curie temperature and the percentage of atomistic bonds lost on the surface as a function of grain size, which can be extended to apply to not only L1 0 -FePt but also generic magnetic systems of any crystal structure. In a recording medium, the inevitable grain size dispersion leads to an irreducible contribution to the dispersion of the Curie temperature. Therefore, our paper gives insight into finite-size effects, which have been predicted to be a serious limitation of HAMR.