There's a fine line between a hesitation and a stall in my opinion. You can get hesitations ranging from slight to deep. If its too deep, it can turn into a stall. Anyway, when an engine is cold, it requires a more fuel for a richer mixture, and a higher idle speed to reduce the risk of stall.

Fast idle and idle control is determined by the air regulator, the Auxiliary Air Control (AAC) valve and the F.I.C.D. (fast idle control device) valve. These items are located at the back left (right if your standing in front of the car) of the engine, behind the inlet manifold.

The system works like this. Air is taken from left hand main air feed pipe (on the NA this pipe connects to the inlet manifold, on the TT the pipe is the one that is connected to the air output of the left hand turbocharger) via a 1 inch external diameter pipe and routed to the back left of the engine, then to the air regulator, Auxiliary Air Control (AAC) valve and the F.I.C.D. valves, then eventually into the centre of the balancer tube. The functions of the 3 valves are as follows:

Air regulator valve- opens when the engine is cold, to fast idle the engine. It contains a thermostat arrangement and an electric heater element which forces the thermostat to gradually shut off the air supply. The air regulator heater element is switched on by the fuel pump relay, which in turn is operated by the ECU.

Auxiliary Air Control (AAC) valve- This is under the direct control of the ECU, and is for fine adjustment of the engine idle speed. It is pulsed on & off to bring to idle to what is set in ROM. Notice it has screw in it. This sets the minimum the idle speed. The ECU computes engine speed from input from the crank angle sensor, so if you are also having idle problems, it could be the crank angle sensor & circuit, in which case you may be experiencing hesitation due to misfiring.

F.I.C.D. valve- This is also under the direct control of the ECU. It is turned on to bring engine speed back to the correct idle speed when the air conditioning compressor is switched in. If your engine stalls when you hit your air con or demister switch, this could be your culprit.

If any of these items are faulty, it's likely you'll experience problems when the engine is cold. Pages EF & EC 154-159 in the manual describe test procedures- electrical tests and checks for clogging, broken springs etc.

To get the connectors off the AAC and FICD valve, I recommend the rubber hoses be removed first. Otherwise it's almost impossible to get the connector clip undone (took me an hour).

If everything checks OK at this point, then do the ECU diagnosis, as described in section 6.