If the coolant temp is faulty = does not read temp properly = temp gauge is not reality
If coolant temp is faulty, computer reading is not correct as well and temperature/air intake/fuel feed ratio might be screwed up. But you see steam, like if engine is hotter then it is usually, not sure if computer bad reading can lead to this...
Like above, if you have boiling coolant liquid, it means bad thermostat, bad coolant pump or bad radiator.
But a combination of both coolant temp sensor and thermostat failure at same time, not lucky.
1993 (build 93/05) 525i automatic M50TU (vanos) 263K miles (ca. 423000 km) in Montreal, Canada (bought the car 9 years ago in San Diego, CA)