Hi-R polyisocyanurate foil-faced insulation board 1-inch thick would not melt and it would provide an R-value of R6 to help keep the heat from passing through the few square feet of the backing wall. In fact, this foam board comes adhered to sheetrock ttha can be applie over the whole wall. However, it is cheaper to cut the upper molding area away to pour or even hand-apply cellulose insulation to drop down inside the wall and permanently insulate it. It could be done part-time easily.