On my Mule (last year I put an egt and boost guage on it) I let it idle down to 320 that is about low as it will go unless it is cold out side. Before the egt gauge if I was driving it in the city I would shut down the engine right away if I had the Mule on the highway I would let it idle 5 minutes at rest areas or fuel stops( I had over 200,000 miles on it when I installed guages still have original turbo).
On the Freightliner I shut it down right away if I been driving at least 5 minutes off highway but let it run at rest areas(original turbo 178,000).
On the Mule at rest areas that it takes abouty 5 minutes to get the tempature down to 320.