  We consider time dependent correlation functions of non-abelian gauge fields
at finite temperature. An effective theory for the soft ($p\sim g^2 T$) field
modes is derived by integrating out the field modes with momenta of order $T$
and of order $g T$ in a leading logarithmic approximation. In this effective
theory the time evolution of the soft fields is determined by a local
Langevin-type equation. As an application, the rate for hot electroweak baryon
number violation is estimated as $\Gamma \sim g^2 \log(1/g) (g^2 T)^4$.
Furthermore, possible consequences for non-perturbative lattice computations of
unequal time correlation functions are discussed.
