  In spite of extended efforts, detecting thermoelectric effects in
superconductors have proven to be a challenging task, due to the inherent
superconducting particle-hole symmetry. Here we present a theoretical study of
an experimentally attainable Superconductor -- Quantum Dot -- Superconductor
(SC-QD-SC) Josephson Junction with highly tunable thermoelectric properties and
a thermal response that is far larger than previous suggestions. The QD energy
level between the SCs breaks particle-hole symmetry in a gradual manner,
allowing, in the presence of a temperature gradient, for gate controlled
appearance of a superconducting thermo-phase. This thermo-phase increases up to
a maximal value of $\pi/2$ after which thermovoltage is expected to develop.
Using time-independent Keldysh countour Green's functions we derive the exact
thermo-phase and thermal response on the junction. These are shown to be orders
of magnitude larger than usual SC tunnel junctions with a sharp dependence on
gate voltage.
