I am not so sure its the ICM under the hood but more likely a wire in the wiring harness.

This year car is know to have harness issues. I have seen it on my car, that its a wire running to one of the sensors along under the intake manifold, and up to the gray connector on the firewall.

The next thing it could be a faulty terminal in the connector to the AMM. It sound there for a moment you were in limp mode as if it had become partially disconnected.

Be really suspicious of a bad wire touching more bad wires in the harness.
They call it biodegradable insulation on the board.

I blame it on engine cleaners soaking under the wrapping. Time and engine heating along with a petroleum product made to emulsify oils and what is insulation but a petroleum product also.

I cut in at the top curl by the firewall and spread it open. Saw a bad guy in there.
I soldered on a new wire and pulled it down and out of the harness at the front sensor.
Patched the new wire in and wrapped up that area with translucent silicone self sticky stretch tape.

That way it reminds to keep looking through it. It's been a couple three years since I did that.

I do not think it was the front sensor but that wire must have been touching another bad spot on a more important friend! Like maybe a hall sensor wire from the distributor that goes to the ICM or others to the ECU.

As far as new paste on a heat sink, I think you would have to open the unit up to find that guy, though it could be an issue. Lucid is pretty sharp on early cars. He may have seen things in that area as well!
By the way it's not recommended, in the Bentley, to just unplug that ICU.
Chrysler wisdom was use there. One time use terminals for what ever weird reason. Like in the fifties, they used left hand threaded lugs nuts ONLY on the left side of the car!

Good luck at exploring around!
Phil