  We investigate the statistical fluctuations of currents in chaotic quantum
dots induced by pumping and rectification at finite temperature and in the
presence of dephasing. In open quantum dots, dc currents can be generated by
the action of two equal-frequency ac gate voltages. The adiabatic regime occurs
when the driving frequency is smaller than the electron inverse dwell time.
Using numerical simulations complemented by semiclassical calculations, we
consider both limits of small and large number of propagating channels in the
leads when time-reversal symmetry is fully broken. We find that at intermediate
temperature regimes, namely, $k_BT \alt \Delta$, where $\Delta$ is the mean
single-particle level spacing, thermal smearing suppresses the current
amplitude more effectively than dephasing. Motivated by recent theoretical and
experimental works, we also study the statistics of rectified currents in the
presence of a parallel, Zeeman splitting, magnetic field.
