Elasticity is property by which a material returns to its original shape after a stress applied on it is released.
Modulus= Stress/strain .
More modulus ( youngs modulus), more is elasticity.
When stress is constant, modulus inversely propotional to strain.
Strain = increase in length / original length
At high temperature the material expands( called thermal expansion of solids). For higher temperature, increase in length would be more as material expands, hence strain would be more.
Consequently, modulus of elasticity would decrease(Since stress is kept constant, and modulus of elasticity is inversely propotional to strain). so, more temperature, more strain, less modulus , less elasticity. Substances with higher modulus of elasticity are more elastic. Hence increase in temperature should decrease elasticity of material.
ANOTHER EXPLANATION
Materials are made of smaller structures called crystals( you will study it in class 12 , chemistry). These crystals have definite shape at given temperature. At higher temperatures, bonds between crystals become weak. So, same stress will produce a much larger strain, and crystals are not pulled back to same position, as intermolecular forces are weak, as said above. So, elasticity decreases at high temperatures.