Car was making this awful squealing noise

I replace the alternator, and serpantine belt yesterday as the car was making this awful squeeling noise and the alternator was not charging as it should. Eventully resulting in it not charging at all. The mechanic said when it did run before he replaced these things he could watch my engine run but my belt would not turn. I got it back yesterday and it drove home fine. I started it this morning it was about 25 degrees last night and after about 1 monute of running the belt started to make the same noise again, after about 5 minutes of driving and the noise getting worse the noise stopped. During the noisy time I would say the lights were somwhat dimmer also, as thought the car were under some sort of load. What the heck it the problem my guess it if gone unchecked I will wreck the belt and alternator again along with some other more expensive parts?