  We study a charged Brownian gas with a non uniform bath temperature, and
present a thermohydrodynamical picture. Expansion on the collision time probes
the validity of the local equilibrium approach and the relevant thermodynamical
variables. For the linear regime we present several applications (including
some novel results). For the lowest nonlinear expansion and uniform bath
temperature we compute the gradient corrections to the local equilibrium
approach and the fundamental (Smoluchowsky) equation for the nonequilibrium
particle density.
