  The control of thermal fluxes -- magnitude and direction, in mesoscale and
nanoscale electronic circuits can be achieved by means of heat rectification
using thermal diodes in two-terminal systems. The rectification coefficient
$\mathcal{R}$, given by the ratio of forward and backward heat fluxes, varies
with the design of the diode and the working conditions under which the system
operates. A value of $\mathcal{R}\ll 1$ or $\mathcal{R}\gg 1$ is a signature of
high heat rectification performance but current solutions allowing such ranges,
necessitate rather complex designs. Here, we propose a simple solution: the use
of a superconductor-insulator-superconductor (SIS) junction under an applied
fast oscillating (THz range) voltage as the control of the heat flow direction
and magnitude can be done by tuning the initial value of the superconducting
phase. Our theoretical model based on the Green functions formalism and
coherent transport theory, shows a possible sharp rise of the heat
rectification coefficient with values up to $\mathcal{R} \approx 500$ beyond
the adiabatic regime. The influence of quantum coherent effects on heat
rectification in the SIS junction is highlighted.
