I would check the connector to make sure it fully seated on the thermostat. And check the pins. If that all looks ok I would check for voltage at the connector which should always be there and the DME controls the ground for the circuit and switches it on via ground.
Here is some info on it, maybe it will help.
2003 BMW X5 4.4i (E53) V8-4398cc 4.4L DOHC (M62 TU)Vehicle
» Engine, Cooling and Exhaust
» Cooling System
» Description and Operation
- Description and Operation
See: Powertrain Management\Description and Operation\Engine Management (DME Motor Electronics ME7.2)\Digital Motor Electronics\Sensors\Characteristic Map, Cooling
Description and Operation
There are two types of thermostats in BMW cars, the mechanical type, arid the type that is electrically heated. Both are designed to bring the temperature of the coolant up to operating temperature quickly.
When the engine is cold, the thermostat is closed; in the closed position, it sends coolant from the engine back to the engine, through a bypass; as a result, the coolant temperature rises quickly. As the coolant reaches the rated temperature, the thermostat gradually opens, to allow coolant to flow from the engine to the radiator.
ELECTRONICALLY HEATED THERMOSTAT
The heated thermostat is both a conventionally functioning and ECM controlled thermostat (two stage operation).
ECM control causes the thermostat to open sooner than the mechanical thermostat rating. This provides sufficient cooling for full load and high output conditions.
The thermostat begins to open at 103°C . This is at the inlet side of the water pump and represents the temperature of the coolant entering the engine.
Before the 103°C temperature is realized, the coolant is circulated through the engine block by the water pump.
After the temperature reaches 103°C it is maintained as the inlet temperature by the thermostat. The coolant temperature at the water pump engine outlet is approximately 110°C . The additional 7°C is achieved after the coolant has circulated through the block.
The operating temperature of the engine will remain within this range as long as the engine is at part load conditions.
ECM CONTROLLED FUNCTION
The map controlled heater in the thermostat will switch ON under the following conditions:
- Load signal "ti" > 5.8 ms
- Engine temperature "tm" > 113°C
- Intake air temp> 52°C
- Vehicle speed> 110 mph
When the heating element is switched ON, the thermostat is heated higher than the temperature of the coolant.
The thermostat opens sooner causing additional coolant to circulate through the radiator which brings the temperature down.
The temperature of the coolant at the inlet side of the water pump will drop to approximately 85°C and the temperature at the outlet side of the water pump will drop to approximately 103°C .
- If the coolant temperature is below 85°C , the heater will not switch on for any condition.
- The display characteristics of the temperature gauge in the instrument cluster have been calibrated to the higher engine temperatures.