Those are OIL TEMPS on the gauge below the tach. There is no coolant temp gauge on the E9x.
My 07 has an oil cooler - Sport package + 18" wheel option = factory oil cooler. I see 230-250 on the gauge after long periods of driving, but haven't hit the track, yet. You can easily see 290-300F oil temp on these cars on track, but remember that's also the oil temp in the pan - the hottest point. After the oil cooler and back into the engine is still probably about 240F.
E92 335i/6MT Dinan Stage 3: intercooler, oil cooler, intake, flash, exhaust, LW dual-mass flywheel.
Vishnu PWM methanol custom trunk mount, Diffsonline 3-clutch Salisbury custom diff, Ohlins Road and Track coilovers, Vorshlag camber plates, much more...
E28 M5 w/ buncha stuff, R171 SLK350