Why does the car run cold air when its idling, but after 4 minutes of starting it runs warm air?

Possibly an idle air motor for your idle problem or a vacuum hose off.

U could be run on eco a/c where the engine is using the power until it has extra to spare. Warm at start could be simlarly that there is now cold air yet and has to "make" cold air to distribute when ready. See if u can find a setting for reg use. cheers, ps eco saves dollars/euros.

The carb has a 5 minute high idle till warm. as for the running rough might try to rebuild it.

the idle air control valve may be bad or just needs cleaned out. idle air control valve acts the same as a choke. if it is messing up it will cause engine not to run right.

Is the car idling faster than it has in the past when cold? The car is designed to idle a little faster than normal during warm up, to warm the engine quicker, and to keep it running. The fuel/air mix richens, (more fuel in the mix than normal), during start up conditions, and then as the engine warms, it should idle down to normal. Have you allowed it to continue its fast idle to see if it idles back down? Your post indicates that you turn it off and re-start to prompt the car to idle down. You have electronic fuel injection. The system adjusts to the prevalaint conditions to give you the perfect mix regardless of the condition it is presented with. It gathers input from a series of sensors that detect engine temp, outside temp, humidity and air pressure, to deliver the mix it needs. Often, when the mix is off, it is a result of a faulty sensor. This can be detected by running a fault code diagnostic check. You can have this performed for free at most national parts chains such as advance or auto zone. Other factors can cause an improper mix, such as dirty or clogged injectors, and/or a dirty air filter. Good Luck! I hope that you find this to be very helpful!

tune up, fuel filter, air filter, dirty throttle body, put good one to gas fuel injector cleaner.

sounds like the idle control vale is sticking when it is cold. It is located on the throttlebody right at the air inlet

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