2002 Mustang V6 squealing sound

I have a 2002 Mustang V6, about 100K miles. Several weeks ago it started making a squealing sound when I would crank the engine. This squealing sound would continue for a while, about 5-10 minutes until (apparently) the engine warmed up (?). At an oil change place, I was told that the water pump had gone bad and needed replacing. I replaced the water pump, but the noise continued. I also needed a new drive belt, and replaced this also, but noise is still there. Sometimes, when the squealing is happening, the car can also just stop. This only happens when at a light (or idle). After the car has driven for 5-10 minutes these problems seem to go away. If anyone can diagnose this and tell me what I can do to check or fix this, I would be very thankful!