Q:

Ohm's law in metals

is Ohm's law valid in metals at ALL temperatures or for a given temperature, it is always valid?
Where I am strugging is that for a given temperature, V-I could be linear with certain contant value of $R$, but if you change the temperature, resistance would change so for that temperature, again V-I would be linear but with different constant value of $R$?

A:

Ohm's law $V=IR$ can be traced to the relation $\mathbf{j}=\sigma \mathbf{E}$, that is, the current is linearly proportional to the applied electric field. 
It is important to note that $R$ (or $\sigma$) depending on temperature, pressure,  humidity, time, etc. does not contradict Ohm's law. Said otherwise, linear response can hold true for different temperatures, pressures, etc.
What does contradict Ohm's law is a nonlinear dependence of the current on the voltage. This happens in many common circuit components. For example, diodes often obey $I = I_0e^{a V}$  instead of Ohm's law.  Transistors and other components have other even more complicated relationships. 
The essential point here is that Ohm's law is that current is linearly proportional to the electric field. It is almost always valid for low enough electric field,  but how it breaks down depends on the system. 

