What is the normal water and oil temperature for the E46 M3?

What about trackdays - how much higher is the temperatures then?

Water temperature is not shown numerically. Fully warmed-up oil temperature for me is about 185-215 depending on driving environment. I've never done a HPDE but I've done some pretty hardcore spirited driving; oil temps have never gone above 215-220.

I just did an event in the upper 80s low 90s and the oil temp would reach 240ish while the coolant temperature never rose above the half way mark. BMW really over engineering the cooling system. If i back off on the straights for a lap or two the oil temp would drop, but i don't think these oil temps are problematic.
What really becomes a problem is after you pull into the paddock after a session and turn the car off. There is no cooling and the motor gets heat soaked. If i don't leave my hood open oil temp will reach the 300 mark, just sitting around.

normal driving ... the oil temp was straight up. only on the hottest of days in stop/go traffic it would be slightly right of straight up.

track days during hotter days... oil temp would reach as high as 275, maybe slightly over, but when i saw it get that high, i would back off and let it cool down some. after all, i'm not out there to prove anything or race anyone, just to enjoy some spirited driving.

Do you all run the original oil cooler?

I see around 240-250 for oil temps. Coolant needle was coming off of 12 o clock and going to the white dot before the red zone. I started lifting down the straights then. It was 92 degrees out, 4500 ft above sea level, track temps were 135. Totally stock...

Do you all run the original oil cooler?
Yes