My lawnmower has a 16Hp Briggs and Stratton engine. I would like to know the correct setting for the coil. I currently have it set at .010.
The lawnmower won't restart after it has been running for awhile. After it cools down it starts okay.

If you can slide a business card through it you are fine.

Common ranges are 0.006 to 0.010 and ALSO 0.010 to 0.014, the use of a business card as suggested by esquire1 is a good substitute for using feeler guages. So at 0.010 you should be o.k.

Seeing how our feeler gauges at the plant are always missing, we use the card trick.

What would cause it not to start after running for awhile? The air filter is clean,spark is good, changed fuel selanoid,fuel filter. Could coil be braking down when hot? How do I check the coil?

Yes, the coil could be breaking down. After it dies, remove the spark plug, reconnect to the spark plug wire, hold the spark plug against the block of the engine, have someone turn over the engine with the ignition switch and see if you see spark. If no, coil is bad.