We consider the random field Ising model on Z^2 with external field i.i.d. N(0,\epsilon). I will present a recent result that under nonnegative temperatures, the effect of boundary conditions at distance N away on the magnetization in a finite box decays exponentially. This talk is based on the joint work with Prof. Jian Ding. In the first lecture, I will focus on the perturbative analysis, which is a crucial tool used in our proof, and similarities in the proofs of the zero temperature case and the positive temperature case. In the second lecture, I will show the significance of applying the Aizenmann-Burchard result to our proofs. If time allows, I will also talk about some new tricks involved in the positive temperature case proof.