When is Ohm's Law not followed?

If it is not a metal at a constant temperature.

Generally if the temperature varies then so will the resistance. This applies to most conductors.

Ohm's law is only followed a minority of the time. Filament lamps do not follow Ohm's law as they increase in temperature, the resistance increases. Other components with semiconducting properties also do not obey Ohm's law - such as NTC thermistors and Light Dependent resistors.

Ohm's law states that for a conductor the current (I) passing through it is directly proportional to the potential difference (V) across it, provided the temperature remains constant. Constant temperature implies constant resistance.

If the conductor heats up the resistance is no longer constant, thus Ohm's law is not obeyed.