The best place to monitor temp is the pan. That’s the best place to get a good average temp. Don’t use the line pressure tap, there is zero fluid flow, you will be basically reading the temperature of the case. The cooler line out of the trans to the radiator will be the hottest fluid, that’s basically the fluid coming out of the torque converter.
I wouldn’t worry until the temp gets over 230-240 continuously. It might get that hot if your really working the truck, but ideally it will cool back down once you start moving and the converter locks. Obviously, the lower the temp (within reason) the better.
Adding a big cooler is always a good idea. If you drive the truck in cold climates, keeping the radiator cooler is a good idea. That prevents the fluid from getting too cool.
Just as a data point for temps...
I had the 6L80E in my 2011 Suburban go out last year during a family camping trip while pulling through the mountains in Montana. Fully rebuilt the trans with some slightly upgraded bits and added the factory tow package radiator, engine oil cooler, and external trans cooler(in addition to the radiator cooler it had before). Last week I pulled the same trailer through the Sierras in Northern California. It was 90-100 Degrees out and ~11% grades for several miles pulling through 8000ft passes. I ended up having to slow to 35-40mph floored and both the engine and trans got up to around 240 degrees before we peaked through the pass and both came back down within a minute or two. The engine comes back down to 210 and stays there unless its under a massive load. The trans runs about 100 degrees above ambient with a small external cooler and a decent load on it. Maximum load and the external cooler just couldn't keep up in those temps. Pulling back through the mountain passes in southern Oregon at midnight on Monday, it was 50 Degrees outside and the trans temp never got over 175 degrees and the engine temps were locked in at 210.
I know its a different trans, but the ideas are the same. You need to size an external cooler for the worst case scenario. If its hot outside, pulling a load, with restricted airflow due to slow speeds, you need a LOT of external cooler to dump the heat. Its even worse in the older transmissions(like the 700R4) where there are big issues with towing in OD and potentially with the torque converter unlocked. The 6L80 is designed to tow fine in OD, the 700R4 is not. It also doesn't have enough gearing or power to pull even a slight hill with the torque converter locked, which just adds to the heat. Get yourself a True-cool 40k external cooler and only tow in 3rd and it will live a long life.