When I turn the engine off the cooling fan is not stopping for a good period of time. at high revs. it's cold it shouldn't start so often. I know the flywheel needs replacement. Can this be the fault? What else can be?

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A sticking cooling fan relay ! What year is your swift ? The ECT - engine coolant temp. sensor is an input to the PCM - engine computer ,when the engine temperature reaches 213 degrees ,there about ,the PCM will supply a ground to energize the relay turning on the cooling fan . Also when this happens the PCM will raise the idle RPM to compensate for the load on the engine . Do you know what a relay is ? It is probably located in the under hood fuse / relay box . It will give you a diagram in your owners manual >

I passed this question the first time I read it, so I will take a stab at it now.
The fans don't come on until the compressor has pumped the freon pressure up to say 150 or 200 psi. And the compressor clutch has to have voltage to engage the clutch.
I wonder if the clutch is going and needs 14 volts instead of 12 to engage ? Or the relay that powers the clutch ?
Speeding up the engine would increase voltage from the alternator.
This is assuming the serpentine belt is tight and everything else is working correctly.
I think I would swap the relay with another and put a meter on that circuit to the ac clutch to see what it takes to engage it.

could be head gaskets,, or even a intake manifold gaskey starting to go bad,, but thats the worst at this time to worry about,, try replacing the thermostat first, it could be sticking and not letting the fluids flow,, also,, flush the radiator,, and make sure the cap is in good working order, check the fan to make sure its cycling properly,, stuck relays can often cause over heating,, you can get a compression check to rule out head gaskets,, or you could do this ,, http://www.youtube.com/user/scottykilmer#p/search/0/QA7KVQq9vKA

you can disconnect the fan(s) and run 12 volts directly to the fans to see if they are working...you need to check the following parts: there should be a fuse panel located inside the engine compartment...check the cooling fan fuses, the cooling fan relay, and possibly the cooling fan sensor located on the engine

i cannot specifically point out what the problem might be, but an overheating car---never a good thing. check everything related to cooling. fans, radiator, hoses, waterpump, coolant overflow tank(see if its got a brownish color or looks like there is oil), and check your oil while your at it...

Sounds like temperature sending unit and/ or fan switch/ relay.

There are two fans behind the radiator. One is suppose to begin running when the AC is turned on. The other is to cool the radiator when it gets too warm. Raise the hood with the engine running and AC "on"and see if at least one fan is running.

sounds to me like the thermostat may be stuck. i would check the coolant, fan, and belts.

most likely a thermostat because the pressure on the a\c will be high if engine is over heating or the fans are not kicking on (check fan relay)