Okay, MAF basically ruled out.
Only does it when its warmed up (translates to me, closed loop mode)
I think that would rule out the Throttle position sensor, not only that, you would have other issues such as shifting issues with the TPS out.
Im not leaning to the IAC as I would think that would cause issues whether it was warmed up or not, i.e. in closed loop or open loop mode, but I cant completely rule that out as you stated 'when its warm and you shut it off'. So I guess there is a chance that could be bad or not working as it should.
I dont know what role the EGR would play in that situation so for now I would keep that in the back of my head.
So lets ask now a few basic questions just to try and rule out any freaky stuff.
1. When was the last tune up done? Plugs, wires, fuel filter, etc.
2. Any recent work done to it?
3. When its warmed up, and you turn it off, and start it back up again, can you drive it and if so, how does it run then? Does it shift okay then?
4. Is the Service Engine Soon light on or do you see it flash on and off or anything like that when its running rough?
I cant think of anything else at the moment. Hopefully we can help you get this figured out.