We study lattice SU(2) Yang-Mills theory with dimension d >= 4. The model can be expressed as a (d - 1)-dimensional O(4) nonlinear sigma model in a d-dimensional heat bath. As is well known, the nonlinear sigma model alone shows a phase transition. If the quark confinement is a consequence of the absence of a phase transition for the Yang-Mills theory, then the fluctuations of the heat bath must destroy the long-range order of the nonlinear sigma model. In order to clarify whether this is true, we replace the fluctuations of the heat bath with Gaussian random variables, and obtain a Langevin equation which yields the effective action of the nonlinear sigma model by analyzing the Fokker-Planck equation. It turns out that the fluctuations indeed destroy the long-range order of the nonlinear sigma model within a mean-field approximation estimating a critical point, whereas for the corresponding U(1) gauge theory, the phase transition to the massless phase remains against the fluctuations.