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New radiator, new cap, overheats when driving, but fan comes on when you shut the engine off and runs until it cools off, then the fan shuts off.

 
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sounds normal to me that fan is doing the job, but check fluid, could be airlock and fan senser not picking it up due to lack of fluid.

 
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It could be the temperature fan switch or relay switch.

 
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Thats perfectly normal. Every vehicle needs a cool down. ... Actually.. it should probably have something cooling it down while it is on the road... other wise it will over heat. What i think it is, is perhaps while your vehicle is running, it is keeping the vehicle cooled down, you just hear it more after the vehicle has been turned off.

 
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i would put a new thermastat in it.if you already put all that other stuff on it and it still over heats.you could check you relay that go's to the fans too.

 
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relax...this is perfectly normal...the engine always gets a little warmer on shutting it off...so the cooling fan comes on and does its job!!