With the increase of temperature, the ratio of conductivity to resistivity of a metal conductor

$\sigma =\frac{\text{1}}{\text{R}}=\frac{1}{\rho l\text{/A}}$    

$\frac{\text{1}}{\text{R}}=\frac{\text{A}}{\rho l}$

$\rho =\frac{\text{AR}}{l}$

$\frac{1}{\rho }=\frac{l}{\text{AR}}$

As temperature increases resistance increases

$\frac{\sigma }{\text{R}}\text{ decreases}$