Small Engines (Lawn Mowers, etc.): My lawnmower runs until it heats up then shuts down?, wistle, starter fluid

Question
Good day, I have a Craftsman lawnmower
SPECS:

5.5hp tecumseh engine
engine model 143.975500
22 inch cutting base, push mower.

This mower was given to me as a gift and after using it for quite a while i have found that the mower runs and works great until it heats up.  Once the mower warms up it shuts off and i have to wait about 15-20 minutes before it will start again. It seems to work for about 20 minutes in the evening and about 5 minutes during the day before it shuts down.  So far I have taken the carb apart, it still looked brand new, the needle, float, seat and all other parts were clean as a wistle and in great shape.  I have also replaced the solid state ignition (ignition coil) Part # TEC-34443C, I have replaced the spark plug, air filter, intake gasket, changed the oil and I am using fresh gasoline.  The Flywheel key is in great shape too.  I can't figure out what could be doing this.  Any ideas?  thanks for your help.

Answer
 Hello Quentin:

 Check for Fire at the Plug when the Engine Quits. If you have Fire, then Check the Gas Tank Cap and Ensure it is Venting the Tank Properly. Spray a Small Amount of Starter Fluid Into the Carburator Throat and See if it Starts and Quits. If No Fire, then Disconnect the Coil Shutoff Wire from the Coil. Check for Fire. If No Fire, then the Coil is Heating Up and Grounding Out. New Coils/Ignition Modules can Be Bad right Out of the Box. Check the Compression when the Engine is Quits. Hope this Helps. Let me know what Happens, Please. I enjoy knowing the Outcome. Thanks.

 Good Luck

 Respectfully

 John