Micromagnetic simulations have been performed to investigate the write position shifts in heat-assisted magnetic recording (HAMR) under variation of variables including the thermal profile, write field magnitude, head velocity, media damping, and write field rise time. Simulations reveal that a larger head velocity or a larger media damping tends to shift the write positions towards the heat center. Simulation results are also compared to the predictions of an analytical model based on classical mean-field theory. It is found that, with smaller thermal gradients the analytical model tends to give write positions closer to the heat center; whereas when thermal gradients are larger it tends to shift the write positions away from the heat center. All these effects appear to be dynamic, and can be understood by recognizing the lag between spin temperature and lattice temperature that cannot be captured by the analytical model that assumes equilibrium at all times.