The mechanic just called and said they put another new belt on (for free).
A new one was put on recently and it started squeaking again so we'll see if this corrects the rhythmic squeaking that goes away and then comes back when the engine is cold.
My '06 corolla is kept in the garage. When I start it there is a rythmic squeak. It sounds like a pulley squeaking but my long time auto shop (not Toyota dealer) has installed a new belt and checked every pulley with a stethoscope and can't find it.
The squeak sometimes goes away but returns...