openspaces, sounds like you've checked most of the boxes for normal operating parameters.
I "think" I disagree with benk on the fan clutch being an issue. I'm not certain that you'd maintain proper engine coolant temp if it was failing. And I believe your truck just has an old school thermal clutch, which would sense heat from the radiator, not the small low mount trans cooler. Although replacements are pretty economical.
A larger cooler and or deep pan will certainly help considerably, but I think you also believe that you were not working the vehicle to the point that it should have been overheating the trans.
I think it's worth doing some research on converter lockup. The 4L80 has an electric converter lockup, which could also be faulty, but it appears to be working in 4th gear, correct?
More importantly, I'm pretty certain that with factory programming lockup can only occur in 3rd and 4th gear and 3rd gear it's only at higher rpms. There are several aftermarket lockup switches or programmers that allow for earlier lockup in 3rd and lockup in 2nd as well.
Possible that you were just below the lockup speed/rpms in 3rd and that is the only real "issue."
I'd research and do some test drives first to find what speed/rpm lockup occurs in both gears and compare to the rpms you were running when it got hot before throwing parts at it.
Just spitballing possible causes/solutions. Hope you figure it out easily.
