The red dye in most standard ATF, not synthetics starts to change color at 275 F, it will start to go from bright red to brown above 275 and go solid black at and above 325 F according tp literature I read years ago in a college auto shop class, it was on one of the test questions
My airplane oil cooler thermostat was set at 190 F before opening, it would run from 195 to 220 F once it was operating at or above 1500 RPM for 20 minutes or more regardless of outside air temps. or altitudes
If I could control both my oil temps and tranny temps. precisely I would be happy to see from 180 to 240 F
Hot oil moves easier and quicker than cold oil as well as the volume increases at the same time
I put my tranny temp sender in my old Ram 2500 CTD in the left front corner of the tranny pan, the guys on CTD web site said to mount it in the front servo on top in the 1/8 NPT pressure check boss, I saw no differences in temps between the two