I'm new here so I just read this thread for the first time this morning, and my first thought was "valve adjustment" -- possibly because the other thread mentioning dealers skipping this step was fresh in my mind.
However, the constant in your description is temperature: the problem only manifests itself when warm; the problem manifests itself sooner at higher ambient temperatures; the problem goes away when the engine is allowed to cool. What else changes as an engine heats up? It's a diesel, so there's no worry about vacuum leaks. It
could be something expanding and sticking in the fuel throttle -- but then I would think that would stick open too -- such that it would stay revved up and not shut down when warm. I keep coming up with valves.
I saw one or two others also mentioned valves, but that was dismissed by this post:
Compression would also be an issue any time but usually WORSE for mal seating valves when cold over hot (where they would happily expand and fit their seats nicely, unless the stems are lengthening which is more than an 'adjustment'. Valves usually wear down, not expand along the shaft. It should be throwing white smoke with bad valves as well.)
Unfortunately, that is not an accurate description. Valves don't expand to fill their seats. When valves expand, they do grow lengthwise along the stem -- that's the entire reason for ensuring there is a clearance gap when cold! The clearance will close as the valve heats up and the stem grows. If the thermal expansion of the valve stem exceeds the clearance, the valve does not fully close, compression is lost, power is reduced, and eventually the valve face will be "burnt" -- eroded away due to overheating. The valve is cooled primarily by conduction when closed, so at the moment it stops closing completely, it heats even faster.
Valves and camshafts can physically wear away, causing increased clearances. However, the lubrication system is designed to prevent this. The countervailing action is "valve recession" -- the constant hammering of the valve face against the valve seat gradually deepening the seat. As the seat recedes, the valve must rise higher to close and therefore the stem rises higher, reducing the cold valve clearance gap.
There is a bit of a balance between the forces of wear and the forces of recession. On some engines, one will predominate, but others engines will differ. Variations in metallurgy can even mean differences from cylinder to cylinder within the same engine.
The engine needs 4 things to run: suck squish bang and blow. If the exhaust valves don't close fully, less suck, less squish, less bang. If the intake valves don't close fully, less squish, less bang, less blow.
You can't hurt anything by checking the clearances, and you may prevent serious long term damage even if it doesn't cure the immediate problem, so there's nothing to lose, IMHO.
But that's just my 2¢, and internet advice is often worth exactly what you paid for it.
