The temperature coefficient of resistance of a wire is $0.00125$ per °C. At $300K$ its resistance is $1\Omega$. The resistance of wire will be  $2\Omega$at:

Resistance of wire varies with temperature as $R$$=R_0\left(1+\alpha T_c\right)$ where $\alpha$ is temperature coefficient of resistance.

$\begin{array}{l}\Rightarrow \frac{R_{27}}{R_{T_c}}=\frac{R_0(1+27\alpha )}{R_0\left(1+\alpha T_c\right)}=\frac{1}{2}\\ \Rightarrow T_c=\frac{1+54\alpha }{\alpha }=\frac{1+54\times 0.00125}{0.00125}=854°\mathrm{C}\end{array}$