  We theoretically propose a phase-coherent thermal circulator based on
ballistic multiterminal Josephson junctions. The breaking of time-reversal
symmetry by either a magnetic flux or a superconducting phase bias allows heat
to flow preferentially in one direction from one terminal to the next while
heat flow in the opposite direction is suppressed. We find that our device can
achieve a high circulation efficiency over a wide range of parameters and that
its performance is robust with respect to the presence of disorder. We provide
estimates for the expected heat currents for realistic samples.
