I propose a method, based on a set of Langevin equations, for bringing
classical gauge theories to thermal equilibrium while respecting the
set of Gauss' constraints exactly. The algorithm is described in detai
l for the SU(2) gauge theory with or without the Higgs doubler. As an
example of an application, the canonical average of the maximal Lyapun
ov exponent is computed for the SU(2) Yang-Mills theory.