Below is the link to the Kohler service manual PDF for the K series. The manual has a page to identify and reveal the pedigree of an engine.
An owner's manual for the K series is also available in PDF on the website.

Here is a link that might be useful: K series service manual

Well mownie, most helpful indeed. Engine quits when it gets hot, noticed today. Any ideas?

Well, unless you know for a fact that it is quitting BECAUSE it gets hot, I would check the vent hole in the fuel tank cap to make sure that it is not simply quitting because the fuel tank is unable to vent (usually takes from 10 to 30 minutes for that.......about be same as to get "hot"). Check that vent hole by probing with a small stiff wire.
BUT.........if this engine is newly acquired (you said that) and you know not the last regular use of the engine before you got it.........it would pay you to pull the cooling shield sheet metal off and confirm that no mice have blocked the air ducts with their nests or food caches.

Noted, mownie. Will check those points.

Hi there mownie,

Well, I loosened the gas cap and did 3 acres of lawn with no troubles. I did have a bit of a panic attack though, when it stopped suddenly after 15 mins. Yup, out of gas! Very funny.

Again, thank you for your help.

Ken

If you think that was a panic attack, read on.
I drove my wife's Grand Caravan on part of a trip we took Sunday.
Somehow, I did not get the gear selector seated properly into DRIVE. The first STOP sign I came to, the darned car wouldn't go when I stepped on the gas.
I'm just about to panic when I notice the needle is pointing to.............NEUTRAL.
I sheepishly shift it into DRIVE and we go on our way.
My wife coyly asks "What was that all about back there?"
I said "Nothing honey, your car just shifted itself into neutral to ruin my day." :^)
Glad your day went well.

Well mownie, right on! How would a full-throttle neutral drop have sat with wifey?

My head would be as lumpy as a sack full of walnuts after she got through beating me :^)