  In an unconventional superconductor, the interplay of scattering off
impurities and Andreev processes may lead to different scattering times for
electronlike and holelike quasiparticles. Such electron-hole asymmetry appears
when the impurity scattering phase shift is intermediate between the Born and
unitary limits and leads to an expectation for large thermoelectric effects.
Here, we examine the thermoelectric response of a $d$-wave superconductor
connected to normal-metal reservoirs under a temperature bias using a fully
self-consistent quasiclassical theory. The thermoelectrically induced
quasiparticle current is cancelled by superflow in an open circuit setup, but
at the cost of a charge imbalance induced at the contacts and extending across
the structure. We investigate the resulting thermopower and thermophase and
their dependencies on scattering phase shift, mean free path, and interface
transparency. For crystal-axis orientations such that surface-bound zero-energy
Andreev states are formed, the thermoelectric effect is reduced as a result of
locally reduced electron-hole asymmetry. For a semiballistic superconductor
with good contacts, we find thermopowers of order several ${\mu}V/K$,
suggesting a thermovoltage measurement as a promising path to investigate
thermoelectricity in unconventional superconductors.
