# How to interpret Ohm's law?

I just started learning about Ohm's law and the textbook defines it as:

Provided the temperature is constant, then for an Ohmic conductor the current through it is directly proportional to the potential difference across it.

My question is how to interpret this. Do I interpret it as:

1. "Provided we can get the conductor to keep the same temperature, then if it is Ohmic, Ohm's law will apply."

OR

1. "Ohmic conductors always keep the same temperature."

Because I also just learned about I-V Characteristic graphs, and under the one for the filament lamp it says that its graph isn't straight because of temperature. So if I somehow managed to keep the filament lamp at a constant temperature, would the graph become a straight line? But then wouldn't that make a filament lamp an Ohmic conductor if I interpret Ohm's law as #1 above? So I'm assuming Ohm's law should be interpreted as #2. (But I suppose #1 would still make sense if it wasn't possible to keep the filament lamp's temperature constant in the first place.)