Heat doesn't work when idling

Have you checked the level of coolant? The system my be low on coolant and only flows through the system when the engine is running faster than idle.

I have read that some Jeeps with the 4.7 liter V8 engine have plastic impellers in the water pump that crumble or dissolve over time, reducing their ability to circulate coolant, especially at low RPM's. I could see this causing an engine to overheat. And this can also reduce the hot coolant flow to the heater. I would remove the water pump and take a quick look before buying parts. Good Luck