Hyundai Repair: my tiburon stalling when idle, throttle position sensor, automatic hyundai

Question
I have a 2001 automatic Hyundai Tiburon. I got the car with about 8,200 miles on it and it seemed in perfect condition except that it stalls when idling. It's done it since I got the car and stupid me didn't take it back to the dealership in time. I notice it happening more in cold weather although lately even in warm weather it does it frequently.
I've taken it to about 3 different dealerships and none of them say they can find anything wrong with it. I have had them replace the MAF sensor and I've gotten a new transmission, but those didn't help. Every once in a while I will clean my throttle body and that seems to help the problem for a couple weeks.
It pretty much stalls everytime I'm at stop lights or when i'm coasting to a stop or just driving really slow in a parking lot or something. I have also noticed when I am on the highway the rpms will drop really fast and then shoot back up like it wants to die even though I'm going 60+ mph. I'm not sure if those issues are related but it seems like they are.
It's gotten to the point where I'm scared to drive my car because it sometimes dies in the middle of intersections. Someone mentioned to me that it could possibly be the idle air control valve, but I have no idea.
Any help would be really appreciated!

Answer
Is your check engine lamp on?  My primary suspicion would be the crank sensor, but that will normally illuminate the check engine lamp after the computer sees a couple bad readings.  If the lamp is on, you'll need to read the diagnostic trouble codes.

You might also have a problem with your throttle position sensor or idle actuator.  These would be consistent with a change after cleaning the throttle body, but wouldn't normally cause an rpm drop while cruising at highway speed.

Unfortunately, this is one of those issues that requires the technician to see a trouble code with failure data or feel the problem occur in order to make a reasonably accurate diagnosis.  The list of things that could be causing the problem is significant, meaning that the technician needs to narrow the possible causes to a manageable level.  If you've got no check engine lamp but you can make the stalling occur, take the car to a very good driveability shop or the dealer.  Have an experienced technician drive the car and feel the car stall or attempt to stall.  A good experienced technician may be able to tell what type of problem you're having just by feeling it.  This will help narrow the list of possible causes.