Re: Rough Running, fine when cold
I'd go with the lambda sensor as the offending faulty item.
I have a 2.0TS that had exactly the same symptoms and after buying a £20 OBD diagnostics connector I managed to diagnose the r/h (as viewed from the front of the car) lambda sensor.
As far as I understand it the AFM and the lambda sensors form a closed-loop feedback system that controls fuel-air mixture and also emmissions. If the lambda sensors develop a fault, their output instead of oscillating in order to trim or boost fuel-air mixture, flat lines at either end of it's operating range which in turn tells the ECU that mixture is rich or weak. I think in my case it was showing mixture as rich and so therefore is reducing fuel input causing uneven running and in my case pinking. Of course this will certainly cause lumpy tick-over as if running on 3 cylinders as each lambda sensor controls 2 cylinders and so with faulty sensor, 2 cylinders will be optimally fueled whereas the other 2 will be showing either weak or rich.
Disconnecting the offending lambda sensor may cure the issue temporarily as when disconnected the ECU will show a fault but will also compensate for loss of sensor input by subsituting a middle of the range value which indicates neither rich or weak mixture. Unfortunately, if your ECU hasn't yet detected a fault on this sensor and you don't have the EOBD light on the dash yet, then disconnecting either lambda sensor will almost definately illuminate the engine warning light. Obviously, if you disconnect the first sensor and there is no difference then this one is Ok and so try the other one. If running of engine improves then you've found the fault. It's entirely up to you if you want to try this method but it worked for me.
If disconnecting either of them doesn't work then disconnect the AFM unit as this completely disables the closed-loop system and ECU runs in what I think is called "limp-home" mode where car runs without any mixture tuning but I think exhaust emmisions will go sky-high and it's very unlikely that car would pass MOT in this state but for me this cured poor running and pinking until I was able to replace lambda sensor.