I've been having this problem ever since I got this car in the beginning of this year. The severity of the issue varied quite a bit over this time period, even almost going away at times. Basically, the car "chokes" when throttle is applied when idling stationary. Overall the car goes into this rough idle "state", rising the idle to about 1050rpm and slightly fluctuating around that mark. When I accelerate normally, the RPMs drop almost to zero, sometimes even stalling the engine. Only way to get the car going is to touch the throttle a tiny tiny bit, the RPMs jump up to about 2000 and then I can let in the clutch and take off. After that it drives relatively fine with some extra jerkiness. It only goes into this state after driven for few minutes(1-2 miles, coolant temp gets to the 1st or second mark) and it goes away after few minutes, about the same time as the coolant gauge goes to the normal middle position(might be relevant). What doesn't seem to affect it are outside temperature, gear/neutral, clutch in or out. I already put in a new fuel filter and when I tried cleaning the ICV I found it to be almost brand new(last owner must have tried fixing this problem too). When I changed the fuel filter the normal idle RPM dropped from about 800 to 500 range.
I also have a different issue that might be related. The car won't start after its been sitting for a while after driving, enough for it to cool down but not fully. It needs a minute or couple of cranking before it starts up(with a small white cloud out of the exhaust pipe).

 

Change the coolant temp sensor. I've seen it fix issues like this in the past. May or may not do it on your car but it's worked before and I can guarantee that at some point that sensor will fail. You're heading off a future problem if nothing else.

 

The temp sensor was actually next on my mind. Am I right that there are two? One in front of the engine second in the back? This is for a 2.8.

 

That's correct. Start with the one at the back of the engine.

 

Actually, I'm pretty sure the one in the back has been disconnected for a month. I unplugged it after I was cleaning out the ICV and it was a real pain to plug back in so I gave up. The CEL light has been on since and that was the only noticeable difference. The temp gauge seems to be working fine so it must be picking up it's signal from the front sensor. This makes me thing that the rear temp sensor must have been bad all this time. Will put a new one in this weekend and see how it goes.