Does the exterior of the case get physically very hot? If it does, then your problem is that the case can’t shed enough heat. If the case is mostly cooler, or only has a hot spot in the middle, then it’s an issue with getting heat from the die to the case.
I would be looking at something like a 100x100x3 copper shim, to help with not just moving heat straight from the die to the adjacent section of case, but also spreading the heat sideways. Heat pipes would be nice but 3mm is too thin for a DIY solution.