Small Engines (Lawn Mowers, etc.): Tecumseh 5.0 runs and quits hot, air filter oil, fuel cap

Question
I have a Sears self propelled mower with a Tecumseh 5.0 . It starts and runs, then after it heats a bit it starts to idle surge, the carb linkage goes with the surging causes it to idle up and down and puff black smoke then eventually die completely out. Model # is 917.372490. Has a new plug air filter oil carb and tank flush with needle and seat. could it be the fuel cap? I am not sure if its spark at this time or fuel? can you give me a step by step on how to walk me through the diagnosis on this problem? thank you John

Answer
I am highly suspecting a bad float. Did you take the float and shake it close to your ear and listen for any sounds of fuel sloshing in the float causing it to be heavy, and not closing at the correct time allowing the engine to run rich (too much fuel)? You must listen very carfully. If it checks out fine then check that it's adjustment is ok, the float should be even to the carb body when tipped upside down..Please let me know your outcome.....Tom