The fan comes on when the ECU senses the engine is hot. Check your thermostat. If thats not it, then maybe your radiator (plastic radiators = suck). Its normal for it to stay on a little after your car is off.
I understand that newer (1995 and >) ECUs were programmed to run the fans to cool the engine down. I have a '94 and the fans NEVER comes on while the engine is turned off. But you know your car better than any of us so if it didn't happen before then there has to be something wrong.
Keep in mind that the fans are ECU controlled with feedback from the ECT sensor. If this were my problem I would troubleshoot it by first faking out the ECT so that the ECU thought the engine was always running cooler. Remember this test is ONLY for troubleshooting purposes. Then I would test drive the car in that condition for about 5 minutes and then turn off the engine. Listen and note if the fans comes on. If the fans don't come ON then either your engine is running hotter and/or the cooling system is inefficient in removing the heat.
Here is a link not entirely related to your problem but has some additional information,
My '00 Altima has just over 100K on it and I am having a similar problem except there's one additional symptom here.
When I am driving or idling (it doesn't matter), after a while the engine fan will come on (normal), but then the temperature gauge just goes through the roof for about 15 seconds and then returns to normal. The fan stays on, eventually shuts off unless I keep running the engine in which case it will just happen again about 15 to 30 minutes later.
After long drives the fan will stay on for a period of about a minute after I shut the car off. It did NOT always do this, but I am do for maintenance so I am thinking it's a combination of things .... a/c belt, thermo, sensor. I'll find out soon. I need to take it in to the shop.
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