  We present the $T$-flow renormalization group method, which computes the
memory kernel for the density-operator evolution of an open quantum system by
lowering the physical temperature $T$ of its environment. This has the key
advantage that it can be formulated directly in real time, making it
particularly suitable for transient dynamics, while automatically accumulating
the full temperature dependence of transport quantities. We solve the $T$-flow
equations numerically for the example of the single impurity Anderson model. We
benchmark in the stationary limit, readily accessible in real-time for voltages
on the order of the coupling or larger using results obtained by the functional
renormalization group, density-matrix renormalization group and the quantum
Monte Carlo method. Here we find quantitative agreement even in the worst case
of strong interactions and low temperatures, indicating the reliability of the
method. For transient charge currents we find good agreement with results
obtained by the 2PI Green's function approach. Furthermore, we analytically
show that the short-time dynamics of both local and non-local observables
follow a universal temperature-independent behaviour when the metallic
reservoirs have a flat wide band.
