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when the pcm is reset shouldn't the engine light go off?
Yes, if you reset it with a scanner. Simply disconnecting the battery will not always turn off the CEL. It depends on what code turned it on in the first place.
As to the no idle when hot thing, that can be caused by a bad coolant temperature sensor (CTS). It's the 2-wire(PCM) one, not the one-wire(gauge) one.