If the temperature of a metallic resistor is raised, the product of...

Resistivity $\rho$ and conductivity $\sigma$ are reciprocals of each other.

$\sigma = \dfrac{1}{\rho}$

The product of resistivity and conductivity is $\rho \sigma = \rho \left(\dfrac{1}{\rho}\right) = 1$.

Since the product is always equal to $1$, it is independent of temperature. Thus, when the temperature of a metallic resistor is raised, the product of its resistivity and conductivity remains constant.