I've designed linear power chips They get hot. No big deal IF the design is good. I can't believe AD doing a schlock job. You don't need heat for a part to fail. There are plenty of failure mechanisms that don't involve the chip getting warm to the touch.
The next time you are on an airplane, watch the wing wiggle a bit. You are looking at something that is engineered properly. If the wing was stiff enough not to wiggle, it would be much heavier. It is the same case with your chip. If it ran cool, it would have to be bigger, have a slug in the package, etc.
I would bet AD has burn in data to show their design is good. It is that kind of a company.