  A gas of interacting ultracold fermions can be tuned into a strongly
interacting regime using a Feshbach resonance. Here we theoretically study
quasiparticle transport in a system of two reservoirs of interacting ultracold
fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel
junction. Using the generalized BCS theory we calculate the time evolution of
the system that is assumed to be initially prepared in a non-equilibrium state
characterized by a particle number imbalance or a temperature imbalance. A
number of characteristic features like sharp peaks in quasiparticle currents,
or transitions between the normal and superconducting states are found. We
discuss signatures of the Seebeck and the Peltier effect and the resulting
temperature difference of the two reservoirs as a function of the interaction
parameter $(k_Fa)^{-1}$. The Peltier effect may lead to an additional cooling
mechanism for ultracold fermionic atoms.
