  We study the steady-state properties as well as the relaxation dynamics of
the nonequilibrium interacting resonant level model at finite temperatures. It
constitutes the prototype model of a correlated charge fluctuating quantum dot.
The two reservoirs are held at different chemical potentials---the difference
being the bias voltage---and different temperatures; we discuss the transport
through as well as the occupancy of the single level dot. First, we show
analytically that in the steady state the reservoir temperatures in competition
with the other energy scales act as infrared cutoffs. This is rather intuitive
but, depending on the parameter regime under consideration, leads to a
surprisingly rich variety of power laws in the current as a function of the
temperatures and the bias voltage with different interaction dependent
exponents. Next we clarify how finite reservoir temperatures affect the
dynamics. They allow to tune the interplay of the two frequencies
characterizing the oscillatory part of the time evolution of the model at zero
temperature. For the exponentially decaying part we disentangle the
contributions of the level-lead hybridization and the temperatures to the decay
rates. We identify a coherent-to-incoherent transition in the long time
dynamics as the temperature is raised. It occurs at an interaction dependent
critical temperature. Finally, taking different temperatures in the reservoirs
we discuss the relaxation dynamics of a temperature gradient driven current.
