The correct answer is option 'C' - semi-conductor.

Explanation:
Conductivity is the ability of a material to conduct electric current. In the case of solids, there are various types of conductors and insulators, each with different properties regarding their ability to conduct electricity.

- Super-conductor: Superconductors are materials that can conduct electricity with zero resistance at very low temperatures. They exhibit a phenomenon called "zero resistance" or "perfect conductivity" when cooled below a certain critical temperature. Superconductivity is a unique property that allows the material to conduct electricity with no loss of energy. However, the question states that the material conducts electricity at higher temperatures but not at lower temperatures, which is not consistent with the characteristics of superconductors.

- Metallic conductor: Metallic conductors are materials that have a high electrical conductivity at all temperatures. The electrical conductivity of metals arises from the presence of free electrons that can move freely within the material. These free electrons are responsible for the flow of electric current. Metallic conductors show a decrease in electrical resistance with decreasing temperature, but they do not completely lose their ability to conduct electricity at lower temperatures.

- Insulator: Insulators are materials that do not conduct electricity well. They have very high electrical resistance, which prevents the flow of electric current through them. Insulators do not show a significant change in conductivity with temperature. Therefore, it is not consistent with the question's statement that the material conducts electricity at higher temperatures.

- Semi-conductor: Semi-conductors are materials that have intermediate conductivity between conductors and insulators. They exhibit unique electrical properties that can be controlled by doping or applying electric fields. Unlike conductors, the conductivity of semi-conductors increases with increasing temperature. At higher temperatures, more charge carriers (either electrons or holes) are available for conduction, resulting in increased conductivity. However, at lower temperatures, the number of charge carriers decreases, leading to a decrease in conductivity. This behavior aligns with the question's statement that the material conducts electricity at higher temperatures but not at lower temperatures.

In conclusion, the correct answer is option 'C' - semi-conductor. Semi-conductors are materials that conduct electricity at higher temperatures but not at lower temperatures.