I have a 128i and a performance steering wheel with the handy temperature gauge.
When I start it up in the morning, both temps are at around 30 C.
Within 5 minutes of driving, the coolant temperature stabilizes at 100ish C, but it takes the oil about 10-12 minutes to reach 100ish C. I go easy on it (not more than 3k rpms) during this time.
Once it does, I switch to g-forces display and let the fun begin