A diffusion process of a Brownian particle in a medium of temperature T is
re-considered. We assume that temperature of the medium fluctuates around its
mean value. The velocity probability distribution is obtained. It is shown that
the stationary state is not a thermodynamic equilibrium state described by the
Maxwell distribution. Instead a nonequilibrium state is produced by temperature
fluctuations.Comment: accepted for publication in Acta Physica Polonica
