I suddenly feel quite confused with the simple equation of a body length (1d case) after being exposed to a temperature difference :

L_final=(1+alpha*dT)*L_initial while dT is the temperature difference

I try to use this equation twice -

1. I want to find the length of a body while the temperature is raised.

L_after raising the temperature =(1+alpha*dT)*L_initial

2. Now I want to find its length when the temperature is lowered to the initial temperature back. I definitely know that it should get the same initial size back, but trying to use this equation leads to:

L_after cooling down=(1-alpha*dT)*L_after raising the temperature

And this doesn't give the same initial dimension.

So, i will be happy to hear an explanation about the proper use of the equation.