I sofar didn´t hear of somebody who was able to unplug the heater core, but its worth a try. You did check the heater core hoses in the engine compartment close to the bulkhead that they are not hot?
You could easily disconnect these hoses and flush them with a garden hose, so that you can see if there is something plugging the lines. Most of the time its the heater core itself which is plugged. Don´t know which substance you could use to clean it.
JEEP Grand Cherokee 4.7 Lmtd 2004
HID 8000K in low and fog / Quad Squad member
Monroe Reflex shocks /
Pirelli Scorpion ATR 245/65/17/
Transgo reprogramming shiftkit.