Similar to mine. I have a temp probe on my MT82 and will read 260’s to 270’s after a hard session at COTAMy temp sensor on my MT82 is in the drain hole. Just used a threaded adapter. Works fine and the sensor isn't hanging lower than the lowest point of the car anyway.
As for MT82 temps at Road America... I can max out my gauge at 260*. It's a Glowshift gauge, so perhaps it's not accurate, but I'm positive it's not far off because I can swap the plug in for my other two Glowshift gauges and get the same exactly every time. So either the temp sensors they provide are bad or I'm well over 260* on track with my MT82. I can delay the temp climb with higher gears, but it's inevitable. On the street, the transmission never gets more than 180.