  We discuss heat transport in thermally-biased long Josephson tunnel junctions
in the presence of an in-plane magnetic field. In full analogy with the
Josephson critical current, the phase-dependent component of the heat current
through the junction displays coherent diffraction. Thermal transport is
analyzed as a function of both the length and the damping of the junction,
highlighting deviations from the standard Fraunhofer pattern characteristic of
short junctions. The heat current diffraction patterns show features strongly
related to the formation and penetration of Josephson vortices, i.e. solitons.
We show that a dynamical treatment of the system is crucial for the realistic
description of the Josephson junction and it leads to peculiar results. In
fact, hysteretic behaviors in the diffraction patterns when the field is swept
up and down are observed, corresponding to the trapping of vortices in the
junction.
