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.

PACS numbers: 05.40.Jc, 05.40.--a, 02.50.Ey, 05.10.Gg