Only when car cold eg over night or for the day then starting

Your car cold start valve puts more gas into the system keeping your engine running higher RPM. When you car warms up, the cold start valve will stop working and your car RPM will drop. What you could have is a vacuum hose disconnected which puts more air into your engine - therefore when you press on the gas pedal, your engine would shut off or you find lack of power and then shut off.

engine temperature sensor ? On a cold start the sensor tells the ECU it's cold so the ECU adds more fuel until the engine is warm.

Sorry - I didn't see the vehicle information the first time.

Let me research this - i will get back to you soon.

Check to see if it is getting proper fuel flow with a fuel pressure gauge. Sometimes when defective fuel pumps get warm, they quit working.

maybe slow,cold start,air control valve or,possibly normal for temp in morning,I live in Australia and cars can take ages to slow down in winter eg1 to 3 deg cel...and very quickly warm up in summer..eg....idle slows down in 1/4 time,have a look at the car if you can park it in warmer conds... to see if its quicker as Toyotas do this normally for fast warm up,lastly has it been well serviced...looked after??

Difficult to say,so many things effect the idle.Throttle position sensor,also the egr position sensor,and the mass air flow sensor for just some of the reasons.Check the air filter for blockage first off.Remove the mass air flow and inspect it for forgien matterial that might caught in the sensor.Any check engine lights on?If so,a code reader might give you an idea where to look for the problem.Some parts stores will offer to do this at no cost.But check with a mechanic before you purchase a part from them,to see what you choices are.The coolant sensor would be my first guess,sense the idle does fine after warm up.This tells me the sensor may be out of range,not sensing cold coolant.Let me know how you come out,Let me know if this helps you at all.

Katrina, the fact that your car runs (like a beauty) when shes warmed up, indicates a fuel air mixture problem when cold. Your car is equipt with electronic fuel injection. This system utilizes a series of sensors that detect conditions such as engine temp, outside temp, humidity and air pressure to determine what mixture is perfect for the prevailing condition. For example, on a cold start, the sensors should know that the engine is not up to the proper operating temperature and provide more fuel and less air, (a richer mixture), until the engine warms, this emulates a choke on a vehicle equipt with a carburator. The problem either lies in the sensor itself, or the brain that interprets these inputs to decide what fuel/air mixture to deliver.

try coolant temperature sensor

Try replacing the coolant temperature sensor for the injection system.

Have you replaced your O2 sensor? If not, try that.