For as easy as the ICM was to remove...it wouldn't hurt to have it tested. My understanding is the ICM can be resistance tested with a multimeter (the instructions are in the Chilton manual)... and also the parts store can test them... with the caveat that the recommendation was of the machine says it is bad... have the parts person test a new one on the machine with the same set up to reduce the opportunity for operator error.
Honestly though, I can't tell you yet the heat soak issue is solved. I drove it to the store last night and back home, shut it off and immediately restarted it with no issues... but I'll know more in a week or so.
Mine did well for a few trips after I replaced the starter and solenoid and then started doing it again. No heat shield over that starter which is in a pain in the ass location to get to. I will probably break down and just buy a newer truck once prices come back down out of the stratosphere. I didn't pay anything for the one I have. It was given to me. It started at the home depot and had to have towed back home. Starter kept trying to turn over even after engine off and key out of switch. Now it does it after the thing gets hot. I can make very short trips in it without it happening but anything that is more than about 20 minutes and it keeps wanting to start on its own after I stop and I have to take the battery cable off.