  We investigate the effect of temperature on the dynamic properties of
magnetic vortices in small disks. Our calculations use a stochastic version of
the Landau-Lifshitz-Gilbert (LLG) equation, valid for finite temperatures well
below the Curie critical temperature. We show that a finite temperature induces
a vortex precession around the center of the disk, even in the absence of other
excitation sources. We discuss the origin and implications of the appearance of
this new dynamics. We also show that a temperature gradient plays a role
similar to that of a small constant magnetic field.
