2000 catera cold start idles rough and dies. After a few times it gets warm enough and runs smooth as silk.

Need year/make/model/mileage of vehicle to provide a more specific set of troubleshooting steps.

When was the last tune up? Hard starts when cold are usually caused by fouled spark plugs, worn plug wires, or weak ignition coils. Fuel systems are not as effected by temperature changes as the ignition components.

oxegen sensor?

Could be the fast idle sensor check to see that the vacume line is hooked up properly.

you need to have the codes checked to know what direction to start repairs,Autozone does this for free

replace the thermostat it is probably stuck open flush the cooling system and replace with new antifreeze

It sounds like the timing belt is off a tooth. Did you have it scanned to see what code was in the computer? These engines will surge when the cam timing is off.

Bought a use 03 last week for very cheep because it was idling rough, read in a forum about focus vacuum leaks and to use small burst of starting fluid to find the leak, spray around engine, if you hear the engine level off and run smooth in a particular spot for a few seconds the leak is in that general area, check the hose in that area, i found a large elbow on my pvc valve line was cracked in half, repaired with copper plumbing elbow fitting and silicone. now runs perfect. be very careful with the starting fluid short burst in well ventilated are.

Most likely you have a bad Idle motor which is a small motor mounted on the intake manifold. If the motor can run better with your foot on the gas but dies if removed then it is probably this. This motor is controlled by the OBDII computer which gets it's control signal from the temp sensor which is located either on the radiator or engine block (which could also be bad), if the electric fan (if equipped) turns on then this is not the problem part, but the idle motor is. Another possibility is that you have some bad /cracked vacuum hoses which should be checked for first, before replacing the idle motor.

probably oil, it may be too thick when it's cold but once it warms up it liquefies and your engine runs smoothly. you could try changing oil, I'm guessing if you have a high performance oil the chances this is the problem may be greater since high performance things are usually geared towards working well when everything is hot

you might wanna use a thinner lighter oil