  We demonstrate that measurements of rapidity differential anisotropic flow in
heavy ion collisions can constrain the temperature dependence of the shear
viscosity to entropy density ratio {\eta}/s of QCD matter. Comparing results
from hydrodynamic calculations with experimental data from RHIC, we find
evidence for a small {\eta}/s $\approx$ 0.04 in the QCD cross-over region and a
strong temperature dependence in the hadronic phase. A temperature independent
{\eta}/s is disfavored by the data. We further show that measurements of the
event-by-event flow as a function of rapidity can be used to independently
constrain the initial state fluctuations in three dimensions and the
temperature dependent transport properties of QCD matter.

Nuclear Theory;High Energy Physics - Phenomenology;Nuclear Experiment