  We propose theoretically a thermal switch operating by the magnetic-flux
controlled diffraction of phase-coherent heat currents in a thermally biased
Josephson junction based on a two-dimensional topological insulator. For short
junctions, the system shows a sharp switching behavior while for long junctions
the switching is smooth. Physically, the switching arises from the Doppler
shift of the superconducting condensate due to screening currents induced by a
magnetic flux. We suggest a possible experimental realization that exhibits a
relative temperature change of 40\% between the on and off state for realistic
parameters. This is a factor of two larger than in recently realized thermal
modulators based on conventional superconducting tunnel junctions.
