It stays on until selected off.
The SIB (#32 01 09) is referred to here
Service Information bulletin SI B32 01 09 dated October 2009.
Heated Steering Wheel Malfunction
E90, E91, E92, E93 (3 Series) produced from 9/2008 and equipped with the Heated Steering Wheel (SA 248)
E82, E88 (1 Series) produced from 9/2008 and equipped with the Heated Steering Wheel (SA 248)
Immediately following a cold start, if the heated steering wheel is switched on in addition to other electrical consumers (i.e., heated seats, rear defroster, etc.), it may switch off after 5-10 seconds of operation. This is an intermittent situation. Cycling the key will typically restore function.
For the first few seconds after start-up, voltage levels may dip momentarily when electrical consumers are switched on. If the supply voltage dips below the threshold for the heated steering wheel, it will be switched off.
This situation may be present even if the battery is properly charged and no charging system problems are present.
Replace the steering wheel electronics with an updated part.