As we know that, length of a wire when the temperature increased
$$
L_t=L_0(1+\alpha \Delta T)
$$
where $\Delta T$ is change in the temperature.
$L_0$ is original length,
$\alpha$ is coefficient of linear expansion and
$L_t$ is length at temperature $T$.
Now, $\Delta L=L_t-L_0=L_0 \alpha \Delta T$
Now, Young's modulus $(Y)=\frac{\text { Stress }}{\text { Strain }}$ $=\frac{F L_0}{A \times \Delta L}=\frac{F L_0}{A L_0 \alpha \Delta T} \propto \frac{1}{\Delta T}$
As, $Y \propto \frac{1}{\Delta T}$
So, if temperature increass $\Delta T$ increases, hence Young's modulus of elasticity $(Y)$ decreases.