My car had same effect not too long ago.. It was from lack of coolant, and your also right about the idle, if your down a little coolant, your idle will go nuts.. as i slowly added coolant, idle slowly went to normal. The 2 coolant lines that run to the heater core were the issue. One had a small slice in it, and would only leak when the engine was warm. The area that those lines are in are also tricky to observe when they are leaking.