I want to know the what is the effect of temperature on modulus of rubber, mathematical expression will be helpful
Rubber which is an elastomer behaves somewhat like an ideal monoatomic gas,
inasmuch as (to good approximation) elastic polymers do not store any potential energy in stretched chemical bonds or elastic work done in stretching molecules,
when work is done upon them. Instead, all work done on the rubber is "released" (not stored) and appears immediately in the polymer as thermal energy.
see for details https://en.wikipedia.org/wiki/Rubber_elasticity The Effect of Temperature on Rubber Band Elasticity
The Effect of Temperature on the. Elasticity of a Rubber Band. By: Anu Rajendran, Lauren Janes, Amanda Hermens. http://www.ikon-gallery.co.uk/Repository/ [Broken].