B

Invar is an alloy known for its extremely low coefficient of thermal expansion.
Step 1: Understand that elasticity refers to the ability of a material to return to its original shape after being deformed.
Step 2: As temperature increases, the atomic vibrations within the material increase, which typically leads to a decrease in the material's stiffness and, consequently, its elasticity.
Step 3: Invar, while being stable at low temperatures, will experience a decrease in its elastic modulus with a rise in temperature.
Therefore, the correct answer is that the elasticity of invar decreases with temperature rise (Option B).