The temperature of a wire is doubled. The Young's modulus of elasticity 

We know that, with increase in temperature, length of a wire changes as

$L_t=L_0(1+\alpha \mathrm{\Delta }T)$

where, $\Delta$T is change in the temperature, L_a is original length, a is coefficient of linear expansion and L_t is length at temperature T.
Now, we can write,  $\mathrm{\Delta }L=L_t-L_o=L_o\alpha \mathrm{\Delta }T$

Young's modulus  $\left(Y\right)=\frac{\text{ Stress }}{\text{ Strain }}=\frac{F{L}_o}{A\times \mathrm{\Delta }L}=\frac{F{L}_o}{A{L}_o\alpha \mathrm{\Delta }T}\propto \frac{1}{\mathrm{\Delta }T}$

As,    $Y\propto \frac{1}{\mathrm{\Delta }T}$

When temperature ($\Delta$T) increases, hence Y decreases.