  The phase and thermal driven transport properties of the T-shaped
uncorrelated double quantum dot Josephson junction are analyzed by using
Keldysh non-equilibrium Green's function equation of motion technique. In this
setup, we have shown that the side-attached quantum dot provides an additional
route for electron transmission which is affecting the transport properties by
adjusting the interdot hopping between the main dot and the side dot. We began
with investigating the impact of interdot hopping on Andreev bound states and
Josephson supercurrent. When a small thermal bias is applied across the
superconducting leads, the system exhibits a finite thermal response which is
primarily due to the, thermally induced, quasi-particle current. The behavior
of the Josephson supercurrent and the quasi-particle current flowing through
the quantum dots is examined for various interdot hopping and thermal biasing.
Finally, the system is considered in an open circuit configuration where the
thermally driven quasi-particle current is compensated by the phase-driven
Josephson supercurrent and the thermophase effect is observed. The effect of
interdot hopping and the position of quantum dot energy level on the
thermophase Seebeck coefficient is investigated
