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 Lt=L0(1+αΔT)where, ΔT  is change in the temperature, L is original length, α is coefficient of linear expansion and Lt is length at temperature T.  Now, we can write, ΔL=Lt−L∘=L∘αΔT, Young's modulus   (Y)= Stress Strain =FL∘A×ΔL=FL∘AL∘αΔT∝1ΔTAs,  Y∝1ΔTWhen temperature (ΔT) increases, Y decreases.