What is the significance of the constant temperature reference in ohms law?

Answer 1

As temperature affects resistivity, the resistance of a conductor may change if its temperature is allowed to increase. For pure metal conductors, the resistance generally increases as the temperature increases.

Ohm's Law ('the current flowing along a conductor, at constant temperature, is directly proportional to the potential difference across that conductor') only applies when the resistance of the conductor is constant so, when verifying Ohm's Law, the temperature must be kept constant, in order to keep the resistance constant.

It should be pointed out that the ratio of voltage (U) to current (R) is called resistance (R), and the resistance of a circuit can be found from the equation, R = U/I whether Ohm's Law applies or not -but Ohm's Law itself only applies when the ratio is constant over a range of voltage variation.

Answer 2

Because the resistance of conducting materials vary (in different degree and sense) with temperature.