  We consider non-equilibrium dynamics of two initially independent reservoirs
$A$ and $B$ filled with a cold Fermi gas coupled and decoupled by two quantum
quenches following one another. We find that the von Neumann entropy production
induced by the quench is faster than thermal transport between the reservoirs
and defines the short-time dynamics of the system. We analyze the energy change
in the system which adds up the heat transferred between $A$ and $B$ and the
work done by the quench to uncouple the reservoirs. In the case when $A$ and
$B$ interact for a short time, we notice an energy increase in both reservoirs
upon decoupling. This energy gain results from the quench's work and does not
depend on the initial temperature imbalance between the reservoirs. We relate
the quench's work to the mutual correlations of $A$ and $B$ expressed through
their von Neumann entropies. Utilizing this relation, we show that once $A$ and
$B$ become coupled, their entropies grow (on a timescale of the Fermi time)
faster than the heat flow within the system. This result may provide a track of
quantum correlations' generation at finite temperatures which one may probe in
ultracold atoms, where we expect the characteristic timescale of correlations'
growth to be $\sim 0.1 {\rm ms}$.
