On my E36, it was a short in the heating pad itself that had to be replaced, but it never came on when it warmed up. I would guess its a wiring issue that is affected by heat (expansion) and probably at a wiring connection. The drivers side is also the most used, so the first to wear out. I would check out a wiring schematic and see where this common fault could be.
The electronic seat heating control system monitors the temperature sensor and heating mats for faults. Detected faults are stored in the fault code memory of the centre console switch centre.
The following faults can be recognized:
Short-circuit or line break
Short-circuit or line break of temperature sensors
Break in heating mats
If a break or short occurs at the temperature sensor, the seat heating is switched off in order to prevent overheating. The function LEDs are switched off.
I couldn't view this schematic for the E39, maybe you'll have better luck..