Gas engines and diesel engines, the old ones especially are different animals.
When we start our MH we let it idle (high Idle)for at least five minutes. It often takes more to bring up air pressure. If idling to keep warm, not pc, now of course it is at high idle. You can set high idle with cruise control. low idle can wash the cylinders, I understand. Countless Truckers do this to keep from freezing to death, at stops to sleep or eat. Some big bruiser diesels are hard to start at real low temps, It takes batter for fuel heaters etc.
When we shut down we let the engine idle to cool down the turbo(s). Contrary to waht EPA etc may say. Diesels get hotter than gas engines and you can destroy a turbo by shutting down and letting oil in the tubro bearings coke or cook.
After a long pull, like one we frequently do, and stop at a rest area at top we let it idle for ten minutes. Turbos are costly as are engine rebuilds with seals etc terminally hard and shrunk oor cracked from hot hot hot.
On gas engines with turbos, I will let it idle five minutes too. Don't care what pc says. I burned up the bearings, by using semi synthetic oil and shutting off engine on a really cranked up turbo engine years ago.
As far as gas engines without turbos the issues aren't as sever, however if in a Mh pulling or pushing 30,000 lbs plus, let her cool a minute or two.
In Arizona, near Kingman we pulled a mountain, 100degress, at the bottom, 70, at the top.The engine in our 95 Thunderbird was way in the red. Let it cool a long time and no issues. If I had shut it off, hot, and in the lower pressure air, it would have boiled everything out and warped the heads etc.
If I am going to freeze to death or broil, I'll let her idle.