[dsraven]

my first check would be to see if the alternator is wired correctly. if that checks out correctly with both a visual wiring trace and also a voltage test to check if the wiring is working as it is supposed to with key on and key off. sometimes new doesn't mean correct. if it still has a draw with the key off then the second check would be to remove the alternator and have it tested. the alternator shouldn't be getting warm with the key off, like LG says in post 7.
phungki, post 4, are you asking if the alternator should get warm with the engine running and alternator charging like usual, or are you asking if the alternator should get warm with the engine off and a battery charger connected? if the latter then the answer is no. alternator should not get warm with key off and a battery charger connected. that is why I suggested to check the wiring for a possible crossed wire or a fuse panel error from the factory and also do mechanical tests for what the wiring is actually doing at the alternator plug with key on and key off-alternator plug disconnected while testing for powered circuits and while key on and then with key off.
you could pull the alt for testing but if the wiring to the alt is incorrect for some reason then the alt will test fine. testing it would be for peace of mind so not a bad thing for time spent
have you checked for powered circuits at the fuse panel when key is off? sometimes things get done wrong from factory or maybe a circuit got inadvertently overloaded and melted some circuits together where you haven't seen them yet. pinch points and places where the wiring passes through something like firewall would be a good place to look