Temperature dependence of the relaxation time in Boltzmann equation for impurity scattering in metals Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons?
It seems to me that there is none. But, some people claim that there is.
So if you could explain, how temperature dependence comes into play if it does at all?
 A: 
Is there any temperature dependence of relaxation time in impurity
  scattering of conducting electrons?

Since in the original post, a precise reference (to Ziman’s book) is missing, I presume the referenced material is
  Ziman, J. M. “Principles of the Theory of Solids” (1999), p. 215,
and the question is referring to the “relaxation time approximation” in Boltzmann’s semi-classical approach to transport in electronic systems in presence of static impurities.
In the Boltzmann’s approach, the change in the occupation number of momentum states $| \mathbf{k} \rangle$ due to collisions is obtained by using Fermi's golden rule which yields an integral equation,
$$
\left( \frac{\partial}{\partial t} n_{\mathbf{k}} \right)_{collisions}
=
- \frac{n_{imp}}{V} \sum_{\mathbf{k}'}
[ n_{\mathbf{k}} (1 - n_{\mathbf{k}'})  W_{\mathbf{k}', \mathbf{k}} - 
n_{\mathbf{k}'} (1 - n_{\mathbf{k}}) W_{\mathbf{k}, \mathbf{k}'} ] ~,
$$
where $\frac{n_{imp}}{V}$ is the density of impurities, $n_{\mathbf{k}}$ denotes the occupation probability of the state $\mathbf{k}$ (not necessarily the equilibrium Fermi-Dirac distribution), and $W_{\mathbf{k}, \mathbf{k}'}$ is the transition rate from state $\mathbf{k}$ to $\mathbf{k}'$.
The first term in the sum represents the rate of scattering out of state $\mathbf{k}$ and the second term, represents the rate for scattering into the state $\mathbf{k}$.
Often, one uses a simpler approximation for the collision term, the “relaxation time approximation”, in which
$$
\left( \frac{\partial}{\partial t} n_{\mathbf{k}} \right)_{collisions}
\approx
- \frac{n_{\mathbf{k}} - n_{\mathbf{k}}^{eq}}{\tau}
$$
where $n_{\mathbf{k}}^{eq}$ is the equilibrium distribution function, and $\tau$ is the “relaxation time”. This time scale is roughly equal to lifetime of the electrons due to the impurity scattering [1]. The $\frac{1}{\tau}$ factor is essentially an approximation to the transition rate $W$, through which only forward scattering (no change in the momentum) is kept.
Notice that Fermi's golden rule is only valid at zero temperature. So, strictly speaking, the result above is valid only for zero temperature. Furthermore, Boltzmann transport equation describes a non-equilibrium situation where the temperature is ill-defined.
So, one concludes that, in the strict sense, the relaxation time cannot depend on temperature. It is related to the ground-state (hence, zero-temperature) properties of the electronic system and the impurities.
However*, it is possible to extend the Boltzmann’s semi-classical equations to include quantum effects; for this, one uses a quantum many-body theory and obtains the quantum Boltzmann equations for a non-equilibrium setting in presence of an external field (e.g., an electromagnetic field). Then, the temperature dependence in the parametres appearing in the Boltzmann equation (like the relaxation time) appears due to the initial equilibrium state – i.e., the state of the system before applying the external field. In the current case (where $\tau$ is directly related to the lifetime of conduction electrons), one concludes the microscopic theory of Fermi liquids that $\tau \sim T^2$ at low temperatures; so, $\tau$ would have only a weak temperature dependence.
For details, consult, e.g.,
Rammer, J. “Quantum Transport Theory”, (2004), chp. 10.8.


[1] This part is based on Bruus, H., and K. Flensberg. “Many-body quantum theory in condensed matter physics” (2004), section 15.3. 
$^\ast$ This note is added thanks to a comment by garyp.

A: Ok, so, since nobody is answering, let me try. 
If we neglect everything but electrons we can write for conductivity an integral with derivative of fermi dirac function under it. So, there it is. This derivation is a delta f at T=0, but it gets fuzzier while temperature increases. So in that change lies T dependence, I guess. But, why then Ziman in his book on transport says that there is no impurity scattering temperature dependence?
