A new scheme for the simulation of heat-assisted magnetic recording (HAMR) that systematically includes fluctuating material properties above a predefined length scale, while retaining magnetostatic interactions, is introduced. Renormalized media parameters Ms, Ku, Aex, and αdamp, suitable for useful length scales, are found numerically. These renormalized parameters are then used to model the Voronoi-cell-composed medium in the HAMR simulation. Transition jitters are obtained under various conditions. The results show that moderate maximum temperature of the heat spot, intergranular exchange coupling, media thickness of at least 10 nm, nonzero canting angle of the head field, relatively low head velocity, and large head-field strength are helpful for a successful recording.