2001 S40. Suddenly developed this problem. When I turn the key off, the Electric Fan in the engine compartment (the one on the right side when standing in front of the car) does not shut off. Have to disconnect the battery momentarily, then it will stop.

Pure BS.
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Keeping it running is better than buying new

Maybe everything is working right? The AC has a cooling fan and the fan will keep working until the temp sensor is happy.

There's different circuits for the Electric Cooling fan/AC Compressor.
Is your car a Turbo? A Diesel?
I found an abbreviated wiring diagram for the 2001 S40 at "Volvo Wiring Diagrams". 150 pages no index or component ID pages.
There's different schematics see Page 105,106,107 for EMS2000, Melco 1, and
Melco 2. You have to hunt for component locations see pg 63 +-

Maybe the sensor is bad? It's probably easy to test with a meter, search for the Volvo sensor test info for your car, it may just be a Varistor that you
can measure hot and cold and get so many ohms.

Depending on which circuit, there's a choice of 3 relays in your main fuse block
that could act up: 2/11, 2/13, 2/28

Post back with the URL for a better wiring diagram, and the sensor test info
if you find it. Share the wealth.

Bill

Anyone have a FIX for this....? I am scrambling to cure the same thing. Here is my story this week.

CEL P0118 is ECT circuit is high ( something like that). Well I spent $1000 having a mechanic chase down an erratic high very high like 4000 rpm idle. He changed the ECT in August. New CEL says it is a prob again. I pulled it and did the ohms vs. temp test, but had no spec to compare it to.

Range was 35*F = 5320 ohms up to 212*F = 200 ohms. Everywhere I looked, it seemed my results were logical. I put it back on. I got 16mpg reading on the dash computer, then it jumped to 35mpg... back and forth. After the test drive the car would not start, seemed flooded. 2hours later it started and struggled, but it idled and the exhaust smelled very weird. during all this the radiator fan runs 100% of the time that the key is on. only way to stop it is to pull the relay or - wire on the batt. and now I have CEL P0128 temp sensor low temp? This car is possessed!

I have purchased an OEM sensor (as recommended on another forum) from FCPeuro and a $20 Tstat. Anyone have any thoughts?

Your readings of the temp sensor seem correct.
A code which says the ECT was too high would indicate that the sensor is not grounded.
You should check the ground, and also check the voltage with the car hot, at the ECU ECT sensor input. It should be around 0.5 volts (vs 3-4.5 when cold).

Not sure about the fan running al the time, but that would result from the ECT too low (really hot engine) or the ECT sensor output shorted to ground.
Check the wiring from the sensor.
Or it could be a separate issue, with the fan controller.
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91 245SE AW70, 89 745-16v, M46, IPD, Dependents-00 S/V 40s, Saab 9-3 SC 6sp XWD