This paper deals with the heat transfer monitoring occurring within an inaccessible membrane distillation system. The membrane separates heated sea water and filtered cooled drinkable water. By adjusting the temperature of the incoming heated sea water and knowing its temperature distribution, engineers can keep its temperature within its best operating parameters and avoid hot spots to form. This would help prolong its life cycle and minimize the cost of the distillation process. In particular, we show that an external observation is enough to reconstruct the temperature of the membrane, which is considered as an unknown source term in a parabolic system.