  We analyze the time-evolution of a quantum dot which is proximized by a
large-gap superconductor and weakly probed using the charge and heat currents
into a wide-band metal electrode. We map out the full time dependence of these
currents after initializing the system by a switch. We find that due to the
proximity effect there are two simple yet distinct switching procedures which
initialize a non-stationary mixture of the gate-voltage dependent eigenstates
of the proximized quantum dot. We find in particular that the ensuing
time-dependent heat current is a sensitive two-particle probe of the interplay
of strong Coulomb interaction and induced superconducting pairing. The pairing
can lead to a suppression of charge and heat current decay which we analyze in
detail. The analysis of the results makes crucial use of analytic formulas
obtained using fermionic duality, a ``dissipative symmetry'' of the master
equation describing this class of open systems.
