@BruceWard: Some reading I did (Four Stroke Performance Tuning by A Graham Bell) suggested that coolant temperature increasing after an engine stops is normal.
There's the issue of cylinder wash....I have nothing to back this up but it's generally accepted that diesel engines stand up to excessive idling better than gasoline engines do on account of cylinder wash, isn't it? On the subject: I once heard a fellow from Caterpillar say to avoid extended idling but if an engine needed to be left running for extended periods, to "bump the rpm's up a bit"
For me, a big part of it is how hard it is to start the equipment and how hard the engine was working in the minute leading up to the stop. If it needs a lot of cranking I'm more inclined to idle the engine for short stops and if it's been working hard I'll let it idle for a minute or two before turning it off.
My Chevy welding truck kicks over in an instant and I have no issues with killing the engine for the shortest breaks.
Of course, on cold days....