  By considering an ensemble of Brownian particles suspended in a heat bath as
a thermodynamic system with an internal degree of freedom it is possible to
obtain the Fokker-Planck equation for Brownian motion in a temperature
gradient, by applying the scheme of non-equilibrium thermodynamics. We recover
explicitely the equations derived in particular by Zubarev and Bashkirov using
statistical mechanical and kinetic methods. In addition when the temperature
gradient does not have an externally imposed magnitude we obtain the
differential equation for the temperature field, which is coupled to the
Fokker-Planck equation.
