My son’s 2001 Dodge Neon tends to run hot. The radiator fan comes on while the engine is running, but does not stay on when the engine is turned off, even if the temp indicator is in the range where the fan should be on. Wiring diagram looks like the fan control relay only works when the ignition is in ON or RUN, which would indicate that this is the way the electrical system is designed, but that seems weird…I thought the fan is supposed to operate even if the engine is turned off. We have already replace the thermostat. Any thoughts?
Be sure the cooling system is full, with the cap so close to the thermostat refilling the cooling system can be difficult. Neons do not use an after-run fan.
The last time I saw this on a Neon it was a simple case of insufficient coolant. The reservoir is in an awkward place, under the cowl, and the shadow makes it hard to check visually. You may be low without knowing it.
Improvise a dipstick for the reservoir. Also, when the engine is COLD, open the radiator cap. Coolant must be right up to the top. Add more as needed, remembering to squeeze the radiator hose to expel air.
As Nevada pointed out, A Neon fan will not run when ignition is off.