I think Oakape covered it nicely. Did you read the article I posted from the Boeing Airliner magazine?
So if you were flying today from say KSFO to PHNL you would need to have the APU running by the EEP and then again shut it down when existing the ETOPS area of operations at the ETOPS Exit Point (EXP), or you could just leave it running after you have started your engines at the gate in KSFO and not take a chance on it not starting. Company policy would dictate this procedure. If you were approved for the program as outlined in the article you could operate just like you would in the 757/767.
Had the 737 had some sort of a HMG, none of this would be applicable.