  We analyze thermally induced spin and charge transport in HgTe/CdTe quantum
wells on the basis of the numerical non-equilibrium Green's function technique
in the linear response regime. In the topologically non-trivial regime, we find
a clear signature of the gap of the edge states due to their finite overlap
from opposite sample boundaries -- both in the charge Seebeck and spin Nernst
signal. We are able to fully understand the physical origin of the
thermoelectric transport signatures of edge and bulk states based on simple
analytical models. Interestingly, we derive that the spin Nernst signal is
related to the spin Hall conductance by a Mott-like relation which is exact to
all orders in the temperature difference between the warm and the cold
reservoir.
