Ford Escort Alternator problems

My mother has 97 ford escort that has a problem that has been giving me fits. It has only 41K on it and not the alternator seems to have gone out or that is what I think is the problem. About two weeks ago she called me to come and get her since the battery was dead, a quick jump and we were back up and running. Seeing that the battery was ove five years old, I decided to replace it thinking that was the problem, since once we had her running the alternator was working fine. About a week later the same problem comes up again after she had driven it for a week and the battery was rained again. I gave the battery an overnight slow charge and everythign seems to be working and when I have the battery disconnected the car keeps on running. Can an alternator work while it is cold and then stop working? I rather know this before I pull out the alternator and replace it. What else could it be?

There’s no real need to wonder much about it. Drive it in to any of the major auto parts chains (e.g. Autozone or like). They will test the battery & charging system for free. Obviously they do this b/c they figure next you’ll buy a battery and/or alternator from them.