Dr. Naveen Agrawal at a very elementary level, the exception to the rule on the independence of the scattering τ on temperature for impurities is the τ-scattering by magnetic centers (the Kondo effect) in heavy-fermion alloys.
The growth of the scattering process on the magnetic center can be understood as an increase in τ, with decreasing T around the defect, in which the electrons are magnetized by the field due to the impurity.
Then, as the T decreases, the effective interaction in a cloud of dressed polarized electrons by the magnetic impurity increases.
Theoretical analysis shows that the scattering lifetime for the Kondo case is
τKondo ~ 1 / Ln (μ /T).
It can be seen in the density of states as a small peak.