The V-i graph for a conductor at temperature   and   are as shown in the figure.  $\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)$ is proportional to

 As we know, for conductors resistance $\propto$ Temperature.
From figure  ${\mathrm{R}}_1\propto {\mathrm{T}}_1\Rightarrow \tan \mathrm{\theta }\propto {\mathrm{T}}_1\Rightarrow \tan \mathrm{\theta }={\mathrm{kT}}_1...\left(\mathrm{i}\right)$ 
and ${\mathrm{R}}_2\propto {\mathrm{T}}_2\Rightarrow \tan \left({90}^{\circ }-\mathrm{\theta }\right)\propto {\mathrm{T}}_2\Rightarrow \cot \mathrm{\theta }={\mathrm{kT}}_2$
From equation  (i) and (ii)  $\mathrm{k}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)=(\cot \mathrm{\theta }-\tan \mathrm{\theta })$
 $\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)=\left(\frac{\cos \mathrm{\theta }}{\sin \mathrm{\theta }}-\frac{\sin \mathrm{\theta }}{\cos \mathrm{\theta }}\right)=\frac{\left({\cos }^2\mathrm{\theta }-{\sin }^2\mathrm{\theta }\right)}{\sin \mathrm{\theta cos}\mathrm{\theta }}=2\cot 2\mathrm{\theta }$
$\Rightarrow \left({\mathrm{T}}_2-{\mathrm{T}}_1\right)\propto \cot 2\mathrm{\theta }$