Using an unconstrained three-dimensional micromagnetic model, magnetic hysteresis was simulated in magnetite in the grain size range 0.08--0.3 &mgr;m as a function of temperature between 100 K and the Curie temperature (851 K). For all temperatures in the cubic phase above the Verwey transition (Tv≈120 K), 0.08 &mgr;m grains switched by coherent rotation, and 0.3 &mgr;m grains switched with an intermediate vortex phase. The mode of switching for 0.1 &mgr;m grains was found to be dependent on both field direction and temperature. For all grain sizes in the monoclinic phase below Tv, switching was by coherent rotation, with the domain state rotating in the monoclinic magnetocrystalline anisotropy easy a-plane. Calculations for coercive force (Hc) as a function of temperature display similar trends to experimental data. Below Tv, the model correctly predicts the large increase in Hc. However, the absolute values of Hc are higher than the experimental data. ¿ 1999 American Geophysical Union