True. Oil returns to the trans from the cooler and is routed through the lube circuit in the rear of the trans, then falls to the sump along with oil being shed by internal components. Oil in the cooler lines has either been heated by the converter or cooled by the cooler. Oil in the sump has been returned from internal use and is being picked back up by the pump. Just like an engine with the sensor in the pan or dry sump tank, I want to know the temperature of that oil in the trans.

I'll stick with knowing what the actual oil temp is in the pan. Afterall that's where the fluid being circulated is coming from.

A guy I know, with a Chevy 454 TH400 dualie pickup, placed numerous temp senders in various parts of the system and hooked them to s single gauge through a rotary switch to monitor the temps while towing; wish I woulda written down the numbers cause now I have CRS.

you can check both locations, converter and sump with a single electric gauge and two pickups, using an on/off/on toggle switch to the sending units. best of both information wise.

My thinking is the tranny operates on the fluid that is sucked up from the filter correct?
Not from the converter
If you want to know the fluid temp coming out of the converter and then when it comes out of the cooler measure both

Most of the heat in a transmission is from the converter. Converter design, stall speed and slippage, sprag or not, etc. effects it. How you run the car, foot or transbrake, 2-step or not, etc.,is the biggest influence.

Why monitor trans temp? Just to try to avoid or detect damage? Change the dial according to how hot the oil is? Or to try to maintain a specific temperature for consistency?

The oil coming from the converter is what it is and usually spikes on the starting line when it's slipping the most. I don't know anyone who monitors just that. Bracket racers may monitor the trans temps with a sensor in the pan and adjust the dial or throttle stop accordingly. But some of the guys who bracket and .90 race seriously, monitor oil temps in the engine and the trans, and have heaters and coolers for both so they go into the water at the same temp - or as close as possible - from the first run of the day to the last.

Slightly O/T: is the ATF pick-up uncovered when the front wheels are airborn? It's certainly a concern for engine oil.

not if you are running a deep pan - a stock pan possibly

Since my deep pan didn't have provision for a temp sensor I monitor the line temp from the converter. At first I wasn't sure this was the best place for it. It sure goes up quick making a pass and the 8 in converter makes for more heat than the 9 1/2 in converter that I've tried in my current 580 combo. Obviously this is due to more slippage. I'm guessing if the converter started to go bad, temps would increase 60ft would drop off, trap rpm would increase etc. If one were to log such data it's just another tool in the arsenal for comparison and would help to identify any issues occuring in the entire package we call a race car