Vortex gyrotropic motion was simulated in two-dimensional square magnetic dots of three-dimensional spin vectors of nanometric size. The Landau-Lifshitz equation with exchange and dipolar interactions was integrated at different temperatures with initial conditions consisting in a single vortex shifted aside from the central position. The gyrotropic frequency is computed. The experimental observation that this frequency decreases as temperature is increased is confirmed: we suggest that the reason is the thermal dependence of the damping coefficient in Thiele's equation. Pinning of the vortex-core motion by the underlying lattice is also observed. (C) 2012 Elsevier B.V. All rights reserved.