  We consider optimization of the average entropy production in inhomogeneous
temperature environments within the framework of stochastic thermodynamics. For
systems modeled by Langevin equations (e.g. a colloidal particle in a heat
bath) it has been recently shown that a space dependent temperature breaks the
time reversal symmetry of the fast velocity degrees of freedom resulting in an
anomalous contribution to the entropy production of the overdamped dynamics. We
show that optimization of entropy production is determined by an auxiliary
deterministic problem describing motion on a curved manifold in a potential.
The "anomalous contribution" to entropy plays the role of the potential and the
inverse of the diffusion tensor is the metric. We also find that entropy
production is not minimized by adiabatically slow, quasi-static protocols but
there is a finite optimal duration for the transport process. As an example we
discuss the case of a linearly space dependent diffusion coefficient.
