The thermostat on my F150 (4R75E) is a square device near the trans itself. Two lines feed in and two feed out.
I have a chart on Ford trannies and regarding the 4R544E, it says:
"Cooler flow is controlled by a cooler bypass valve in the main control (which I interpret as internal in the valve body- J.A.) that will not fully open until 100F. Until 100F, there may be flow out of both ports."
It further specs that full cooler flow is achieved at 150-180 degrees.
If the 5R44E is typical of the other Ford trans' I know about, the temp sensor will be in the valve body and the PCM uses that sensor to delay converter lockup until the fluid reaches a preset temp. I have a Gryphon programmer that reads this temp, but I also have a deep pan with a temp sensor installed. Fluid temp in the pan reads about 15 degrees cooler than the valve body sensor. The really hot oil is coming out of the converter and that oil could be 50-100 degrees, or more, hotter than the pan or valve body (the higher numbers in extreme situations).
In an old GM 700R4 I used to have, I installed sensors in the pan, the cooler out line and the return line. The pan could be 165 and the outlet line could be 240 and the return 140F.
A good trans fluid can handle high temps for short periods but it's the time-at-temp which will really kill it. If it comes out of the converter at 240, a good set of coolers can knock 100 degrees off pretty easily, so it doesn't spend much time at that high temp, but the stuff that stays in the converter may spend more time at the French fry temps (though cool oil is being fed in about as fast as the cooler outlet flow is going out).
Anyway, the long-winded bottom line here, it that the temp you see is not the highest temp in the trans. If you keep in the back of your head that the converter is some 50-80 degrees hotter, you'll have some idea when it's time to back off. I don't worry about 220 or so continuous (in the converter) but if you read 200 in the valve body, then you can figure the converter is 250-plus. In short spurts, even that is not all that harmful, especially with a good oil, but I'd be thinking about backing off of whatever work I was doing to cool the "poor bairn" off a little. If you work the trans this way a lot, consider upgrading your coolers.