The thing to remember about the heat sink paste and cooling the ICU, is that the paste doesn't aid cooling or the connection. It's the metal/metal contact that transfers the heat. The heat sink paste helps fill the small voids and prevent corrosion. There is something that supposedly creates a better connection, but don't recall what it is.
In any case, the original paste could have dried out, and if it was really slathered on, could be really inhibiting the transfer of heat. So clean it off well and smear just a thin coating on one side. Remember, this stuff doesn't promote heat transfer, but inhibits it. So don't use much. In fact, it's a good idea to polish the two surfaces, even wet sanding them with fine paper on plate glass, then polish. The more contact surface, the better it cools.
And I agree, these symptoms could be caused by the ICU overheating.