  We analyze heat and charge transport through a single-level quantum dot
coupled to two BCS superconductors at different temperatures to first order in
the tunnel coupling. In order to describe the system theoretically, we extend a
real-time diagrammatic technique that allows us to capture the interplay
between superconducting correlations, strong Coulomb interactions, and
nonequilibrium physics. We find that a thermoelectric effect can arise due to
the superconducting proximity effect on the dot. In the nonlinear regime, the
thermoelectric current can also flow at the particle-hole symmetric point due
to a level renormalization caused by virtual tunneling between the dot and the
leads. The heat current through the quantum dot is sensitive to the
superconducting phase difference. In the nonlinear regime, the system can act
as a thermal diode.
