1992 John Deere stx 38 with a Kohler 13 horse power... issue when the engine gets hot after 15 to 20 minutes of running it dies with a similar sound like running out of gas.

I have check fuel line
I have changed the fuel filter
I have replaced the gas cap

The engine is still shutting down... once I let cool for 5 or so minutes, it starts right back up and runs till hot...

Any advice on what is causing the issue.

I have two things that could cause something like this. I am sure there are other possibilities.

1) Check under the engine cover to make sure that there isn't a bunch of grass or mouse nesting that is keeping the engine from cooling properly.

2) The coil/magnetto could be breaking down when it gets hot. A quick test when the engine shuts down to see if you still have spark could answer this.