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My son bought the noted mower last year and apparently he has only used it a few times and put it up in disgust.It will run fine until it reaches operating temperature and then it will shut down and not crankuntil it completely cools down. Any advice on where to look? It has done this from day one!

Sounds to me like a faulty ignition coil.
buy an Inline spark tester. like this one, or this one

and check for spark after it dies.

Thank you!

Actually you will be better served buying one like below that has a neon tube in it which glows red / orange because you can actually see them in other places like the bottom level of a gold mine .
Fit it so you can see the globe then go mow.
As the mower is starting to die watch the tube.
If it flashes regularly all the way to the bitter end then the coil is good.
If you get irregular flashes or none at all. pull the bower housing off, remove the kill wire from the coil and repeat the above.
If you get the same irregular / lack of flashes as the engine dies you have confirmed the coil is bad
Let us know how you go.
The spark tester is the most used diagnostic tool in my tool chest .
The 3 point is used to test the strength of the spark and the Lise white one is a joke .

Thank you very much! It just bothers me that this mower came from the dealer this way!

If he bought it from a dealer then take it back.
Mower shops can only do a limited amount of testing.
I run a tank full of fuel through everything that I repair because I have a lot of grass to mow and 10 miles of fence to trim under
Most mower shops are in complexes so the best they can do it put the mower is a venting booth and run it for a few minutes .
Could have been bad from the factory