Mower shuts off after running for 20 mins. then you have to wait 10 mins to start again.

Hey John!
Have you check the OIL some of these engine have a low oil shut-off sensor feature built-in ?
Check also that the fuel is not contaminated (Fresh Gas, please!)
Good Luck,
JP

Bad ignition module heating up and failing.

Check the breather in the fuel cap, run it with the cap loose and see if it is any better.

If you have a Briggs & Stratton this problem is there is not enough valve clearance . IT is a major problem with B&S motors as the valve stems stretch with use and the clearance is lost and when hot the valves are held open. Remove the valves and grind the end to obtain correct clearance.

The hot interior is heat failing a relay or module causing intermittent failure .

Check fuel filter, may be clogged.

Sounds like you need to replace the ignition coil,it may have leaked out it's coolant and the it will go to ground when it is hot.

Try changing your inline fuel filter. Sounds like the fuel runs out of the bowl in the carb.

I had the same problem. Turns out,( and I didn't believe it when I was told) but, my problem turned out to be cheap (inferiour) plugs and wired. I was reccomended to use NKG plugs and Borg-Warner wires.

I had the same problem on my craftsman 18.5 hp, the problem was in the choke, the spring was broken, and the choke was not free, replaced the spring and it is fine now. Check it out. Good luck.