This contribution deals with the shape optimization of the cooling process of the glass vase production in this particular system consisting of mould, glass piece, plunger, insulation barrier and plunger cavity, similar to the system described at AMEE' 14. In contrast to the previous problem we apply the insulation barrier located in the plunger cavity to control temperature distribution in the plunger during the press cycle of production in the glass industry. The state problem is given by the energy equation in the whole system. The design variable is taken to be the thickness of the insulation barrier and the cost functional is the squared L-r(2) norm of the difference between a prescribed constant and the temperature on the outward boundary of the plunger. Existence and uniqueness of a solution of the state problem and existence of a solution of the optimization problem are proved.