I am beginning to think it is the heat, but the mower being air cooled there is nothing I can do to correct this.
Ha. Man you want to work fast. :cool2:
1st let me say I am not familiar with your exact mower, I am just trying to help you sort this out.
Don't worry about the heat the air cooled is supposed to handle it. Something else is amiss...
If you suspect the coils or plus wires do this BEFORE ordering parts.
When the sputtering is present and it's "hot" as you suspect shut it off and pull a plug wire off.
Crank it back for just a short time to see what it sounds like running on one cylinder.
If it's way worse, put this one back on and pull the other one off.
This might indicate that it's not firing on one identified cylinder.
A mower will run on one plug but you can SURE tell it when it's missing; especially with the PTO pulling horsepower.
If this test is totally different to your observation of the "sputtering" then the problem may be elsewhere.
Normally if one side is not firing that plug will look way different so I am not sure a coil or coil wire is the problem. (you say both look good)
But the plug would need to be missing for a time to foul the plug up real bad.
You still have no idea if this is electrical or a fuel issue.
Heat will do funny thing related to the coils firing.
With a technical manual which I do not have for you mower, you can check the coils with a meter.
You could test the two coils with the wires off ground to all points and connectors/connectors to see if both test basically the same with no manual.
This might give you an indication. Inspect the plug wires carefully to be sure one has not came apart inside.
BTW "ethanol free" fuel is more important that high octane fuel.
At this point I am guessing you have a carburetor problem, but that is just a wild guess.
With it running put a voltmeter on the battery. What does it read?