The engine must cool down completely before starting work.
The coolant temperature indication system consists of a temperature gauge mounted in the instrument cluster and a coolant temperature sensor unit, usually located on the thermostat housing (see illustration). Some vehicles have more than one sensor, but only one is used by the temperature gauge. On M40 engines, the sensor unit is mounted on the left rear side of the cylinder head.
If you suspect that the meter is not working properly, first check the coolant level in the system. Make sure that the wiring between the sensor and the meter is not damaged and that the fuses are OK. (If you suspect that the fuel gauge is also faulty, the problem is almost certainly in the instrument cluster or its wiring).
Before checking an electrical circuit, refer to the relevant circuit diagrams (see chapter On-board electrical equipment system). If the sensor unit simply grounds the circuit, perform a test by grounding the wire connected to the sensor with the ignition on (but without starting the engine, for safety reasons). If the meter goes off scale, replace the sensor unit. If the meter does not respond, either the meter or its wiring is faulty. Where the sensor unit has two terminals, check the circuit by measuring the resistance of the unit. Exact figures were not available at the time of writing, but normal resistance should be approximately several hundred to several thousand ohms (depending on the temperature). Readings equal to zero (in case of short circuit) or infinity (in open circuit) will indicate a faulty sensor unit.
Do not ground the wire for more than a few seconds, otherwise the meter may be damaged.
If a new sensor unit needs to be installed, allow the engine to cool completely first. Some coolant will leak out when the sensor is removed, so either be prepared to reassemble it or have the new unit ready to install immediately after the old one is removed. Disconnect the wiring, then loosen the screws and lift the old sensor unit off the engine, then install the new one. Apply sealant to the threads. Reconnect the wiring and finally check the coolant level.
[The original version is on the portal: «bmwman»]