Small Engines (Lawn Mowers, etc.): 15.5 HP Kohler dies when hot, blown head gasket, hp kohler

Question
I have a Sears mower with a 15.0 HP Kohler engine. When it is above 80ish outside it will run for maybe 1/2 hour and then die. At that point it will not even turn over. If I let it sit for 1/2 hour it starts fine and will run for at least another 1/2 hour. Any ideas? Oh yeah, last year I had the same problem, but it seemed like it would still turn over. It seems electrical since it won't turn over. I can turn the shaft and there is still compression (last year I wondered if the exhaust valve was heating and not seating right).Thanks for your help.

Answer
Rick, blown head gasket, valves, ign coil, are some of the things....How old is the engine? battery ign or magneto? A  starter motor that won't turn over the eng when hot is a sign of a defective starter or battBattery that goes dead indicates taht the charging system is bad and has battery ignition....what's the batt valtage when it quits.........just to name a few things....Hard to say what's wrong if I do not know the the engine's model and age.  best I can do    bob