  Since its recent foundation, phase-coherent caloritronics has sparkled
continuous interest giving rise to numerous concrete applications. This
research field deals with the coherent manipulation of heat currents in
mesoscopic superconducting devices by mastering the Josephson phase difference.
Here, we introduce a new generation of devices for fast caloritronics able to
control local heat power and temperature through manipulation of Josephson
vortices, i.e., solitons. Although most salient features concerning Josephson
vortices in long Josephson junctions were comprehensively hitherto explored,
little is known about soliton-sustained coherent thermal transport. We
demonstrate that the soliton configuration determines the temperature profile
in the junction, so that, in correspondence of each magnetically induced
soliton, both the flowing thermal power and the temperature significantly
enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat
oscillator, whose frequency is in tune with the oscillation frequency of the
magnetic drive. Notably, the proposed heat oscillator can effectively find
application as a tunable thermal source for nanoscale heat engines and coherent
thermal machines.
