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I am by no mean expert in that field but I will give it a try:
For me it seems exactly what I would expect from a wall with some property of isolation and thermal mass. Thermal mass will store some energy the will slowly dissipate through your outer surface and isolation would delay the energy transfer from side to side. In your case it seems that the inner side is hotter and that is why energy flows outside bound. And by the way your wall is not storing energy. It is losing it.