Take a peek at the TPS (throttle position sensor) if it has a bad spot it can send erroneous signals to the ECM. The ECM doesn't know what's going on and can't compensate. Check it with an ohm meter, resistance readings should go up down smoothly as the throttle is opened/closed. If it skips a spot or blanks out, you got a bad TPS. Heat can affect it, as heat causes material to expand, and it may be causing the TPS to bind.
Also look at the injectors. On the 6's they have asbestos shields around them on the intake manifold, to help block the heat from the exhaust manifold from affecting them. If the shields have deteriorated or are missing, you could be experiencing good old vapor lock.
The fuel is boiling in the lines from the heat at low speeds/sitting still.
When you're running at speed, the fuel is flowing fast enough to not be affected as badly. Slow speed or sitting at idle, the fuel need is less, so the fuel sits and soaks up all that heat. After it runs a while the cold fuel coming in starts to cool the hot lines enough you start getting liquid fuel instead of fuel vapors. The ECM meanwhile is commanding wide open injectors to get the idle back up, and as soon as the cool fuel hits em the idle screams up before the ECM can catch it and adjust it back down.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.