Idling problem

I have a 89 XJ 4.0 w/ AW4, I have had a idling problem for the last couple of weeks, I tried everything to cure it but it still occurs. I even took it to the stealership to have the TPS and IAC inspected and adjusted, no help that was.

Here is the problem , when the motor first starts, when it is cold ,the idle is perfect, once the motor gets warm the idle jumps to 1200rpm. The way to cure this is to just tap the gas pedal and the idle drops down to normal. I have replaced the throttle cable thinking that maybe the culprit, but no cure. I also adjusted the idle adjustment screw on the TB but that just drops the idle too low when it is normal. It may seem like a tiny incovenience but it is a pain, I have to do the right foot tap the gas pedal while the left foot hits the brake to slow down.

Any help is appreciated.

I have cleaned the TB, the IAC and checked vacuum hoses but the prob still persists

Mine did pretty much just the opposite, the idle would start out just fine (around 600-700) and when it got hot, drop down to 3-400.
Don´t know exactly what fixed it. I squirted some penetrating oil down the IAC port, scrubbed out the engine temp. sensor connectors, knock sensor connectors and O2 sensor connector. Problems gone. IAC's get sticky, hard to test for a sticky spot, that only acts up occasionally or only at a certain spot in the piston travel.
Have you checked your intake manifold bolts, possible when the manifold gets hot it leaks vacuum. Also possible the engine temp. sensor or the MAT (intake air temp. sensor) has to much resistance, either in the sensor or the connector. Telling the ECU things are much colder than they actually are.
Try plugging off your vacuum lines one at a time and seeing if you notice any difference. Don´t mess with the MAP vacuum though :laugh3:
I had a few hundred RPM rise in my old 87, turned out to be the TB gasket, it was old and shrank some.
The problem usually turns out to be the last thing you look at, I know not funny.