The elastic modulus is a term used in the formation of the stiffness matrix. Once the stiffness matrix (and load vector) are formed, CAESAR II solves the matrix equation [K]{x} = {f}, for {x}.

If you change E, you change [K], therefore {x} changes. This applies to the hanger load cases as well.

Almost all piping codes state that the flexibility analysis be performed using the cold modulus of elasticity. The exception to this statement is EN-13480 (and those codes based on 13480). However, even these codes don't discuss hanger cases with regard to the elastic modulus.

I suggest you use Ec for your hanger design load cases.