Langevin simulations at finite temperature of two-dimensional magnetic nanodots were performed using the Landau-Lifshitz equation with exchange and dipolar interactions. In a wide range of temperatures, the dynamics of square samples with one central vortex was studied, focusing on the out-of-plane magnetic component at the vortex-core. This vortex-core undergoes polarization sign reversals in a thermally activated process. In the intervals between polarization flips, the out-of-plane spin components at the vortex-core show oscillations with identifiable frequencies connected with certain eigenfrequencies of the system associated with polarity active modes. The vortex-core positions were also monitored.