  We study the diffusion and deformation of classical solitons coupled to
thermal noise. The diffusion coefficient for kinks in the $\phi^4$ theory is
predicted up to the second order in $kT$. The prediction is verified by
numerical simulations. Multiskyrmions in the vector O(3) sigma model are
studied within the same formalism. Thermal noise results in a diffusion on the
multisoliton collective coordinate space (moduli space). There are entropic
forces which tend, for example, to bind pairs of solitons into bi-solitonic
molecules.
