  We study dynamics of an antiferromagnetic soliton under a temperature
gradient. To this end, we start by phenomenologically constructing the
stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid
of the fluctuation-dissipation theorem. We then derive the Langevin equation
for the soliton's center of mass by the collective coordinate approach. An
antiferromagentic soliton behaves as a classical massive particle immersed in a
viscous medium. By considering a thermodynamic ensemble of solitons, we obtain
the Fokker-Planck equation, from which we extract the average drift velocity of
a soliton. The diffusion coefficient is inversely proportional to a small
damping constant $\alpha$, which can yield a drift velocity of tens of m/s
under a temperature gradient of $1$ K/mm for a domain wall in an easy-axis
antiferromagnetic wire with $\alpha \sim 10^{-4}$.
