"I cannnot turn it over until it seem to want to cool down"

TURN OVER means crank.
Start means run-

I'll assume you mean it won't RUN.

There are 2 things that can cause this-
Lack of spark to the spark plugs
OR
Lack of fuel.

The fuel filter should be changed just for normal maintenance!
IF it's too restricted (because that means it's working) there will be insufficient fuel flowing to the carburetor.
The carb runs out of gas and the engine stalls.
Wait for awhile, and the carb bowl SLOWLY fills back up and REPEAT.

The other can be an ignition coil that's bad. Sometimes they get heat sensitive and quit working. Engine stalls, cools off, REPEAT.
Check for spark IMMEDIATELY after the engine dies.

You didn't say how long it runs before the problem occurs or how frequently it repeats???

Anyway, I'd change the fuel filter since it's OVERDUE!

Thanks, Yeah I know the fuel filter is overdue, I will do that. Just pulled the engine shroud off and cleaned the engine from all the clay soil here.
When it stalls, I turn the key and nothing happens, no sound no movement no nothing. Yesterday I mowed for 25 mins and it stopped running. waited 15 mins and started it again with only enough time to run it into the garage.

After cleaning the engine and reading a few of the other blogs I drilled a small hole in the gas cap and it ran for 15 minutes in the driveway with no hesitation. The opening in the gas cap was closed/plugged.

No sound, click nothing indicates an electrical problem, assuming you have disengaged the deck.

IF you are loosing voltage to the carburetor fuel solenoid, the engine will shut off.

I'd suggest checking the connector to the key switch. It sounds like it might be making intermittent contact.
However, the fuel solenoid should also be supplied from the output of the alternator.