BMW Repair: 92 bmw 325i Idle speed, air leaks, bmw 325i

Question
My wife's car overheated, the alt. tensioner pulley seized up both alt belt and a/c belt came off.  She kept driving until she saw that it was overheating.  I made sure there was still oil in the engine so I cranked it up and it was idling in and out like taking a breath 15 seconds into it, to idle speed goes to like 3-4000 rpm's.

Answer
Have all the overheating problems been fixed? The idle problem I have never run into after an overheat. It could be the idle control valve but I am not sure just how high a stuck valve is capable of raising the idle. Also check for any air leaks in the intake boot.
              Kimber