With that much temperature difference between the two cylinders with a thermo-scan check, I am inclined to think there is a problem in the carburetor.
A partially blocked (with crud) main fuel jet could cause this.
Pull the spark plugs and describe the coloration you see on the spark electrodes and cup. You need to keep notes on which plug came from which cylinder.
A bright gray, dull white, or a blistery metallic look are all indications of a "lean burn" which can be due to a blocked jet.
A dull or flat black "sooty looking" color indicates too much fuel (or too little air) being fed to the cylinder.
A shiny black gooey looking coloration indicates oil fouling.
A normal and correct coloration is a dark tan or light brown shade, uniformly dull in appearance.

When I removed the plugs to check the valves I did notice that the plug from the problem cylinder was a very bright gray/brown and the cylinder on the starter side was dark but both fire when I tested. The fuel filter was replaced at the beginning of the season. Since this tractor is a 2003 model are there any isssues with ethanol that seems to be in all gas these days?

After I adjusted the valves it ran well until some heat built up (about 3 or 4 minutes) but there was still a big difference in exhaust temps but reversed from when the bad cylinder was not firing. The "bad" cylinder exhaust was almost 600 degrees and the starter side was around 350. When the off cylider was not firing it's exhaust temp was in the 150 area. That probably does indicate some sort of fuel issue?

Thanks for your help!

I'm now pretty sure it's a fuel/carburator issue of some sort. Today the opposite cylinder is not firing.

Let me see if I have this right.
Did you re-adjust the valves yesterday? and today the opposite cylinder is not firing?
Fuel related loss of "one cylinder", caused at the carburetor can usually only happen if if the carb involved is a "2 barrel" configuration(2 venturi with 2 main fuel jets). And your is that type. But............the defect causing the loss of a cylinder typically stays in the same place and you will not have a different cylinder affected on different days.
Only in cases where water has become present in the tank and carb bowl will you have the chance of a water slug blocking a jet temporarily and then clearing up or the other jet becoming blocked later.
I wonder if you have actually performed the valve adjustment procedure correctly.
I have my own version of the procedure which explains many basics of the 4 stroke cycle that can trip up novice mechanics.
E-mail me if you would care to read my procedure.
Use the forum e-mail feature (the one that you did not enable when you joined, but I did).

Well... adjusting the valves may be too strong, I basically checked the valve lash with a feeler gauge and made sure the lock nuts were tight, they were. The tractor is still running on only one cylinder and the exhaust temp differential did switch from one side to the other. I found that curious as well but it did. I have a repairman coming today to see if he can diagnose the problem.

The carburator was disassembled and there were no obvious problems but he did put a very small probe into each jet, 4 I think and the 2 tubes that hang down, I think they had 8 holes that I think vaporize the fuel. After reassembly, even though nothing appeared wrong inside, the tractor now runs fine. There must have been something in there but neither he nor I saw a thing. Any thoughts/advice?

One more thought about water. I use Stabil year round so I hope water did not contaminate the carb but who knows. The repairman said that Sea Foam was good too.

Those tubes with 8 holes are "emulsion tubes".
These actually mix air with the fuel in the tubes and it results in a "foamy emulsion" of fuel and air. This emulsion is lighter than pure gasoline and thus it will become airborne much easier when it reaches the venturi of the carb.
This helps to ensure the fuel vaporizes better than just tossing drops of pure fuel into the induction air stream.
Slugs of water that make their way to the carb can certainly block the small holes in the tubes. You may not have seen the water but it sure sounds like it might have been the villain here.