  We consider far from equilibrium heat transport in chaotic billiard chains
with non-interacting charged particles in the presence of non-uniform
transverse magnetic field. If half of the chain is placed in a strong magnetic
field, or if the strength of the magnetic field has a large gradient along the
chain, heat current is shown to be asymmetric with respect to exchange of the
temperatures of the heat baths. Thermal rectification factor can be arbitrarily
large for sufficiently small temperature of one of the baths.
