Why does my engine run rough when cold but not when warm?

The catalytic converter needs to warm up to a running temperature and various operation in the engine devote energy or fuel to this process. Once the catalytic converter has reached this "running temperature" it can easily maintain this temperature with the heated exhaust from the engine. One of the "warming up" components is malfunctioning, most likely the pre- or post injection of the fuel into the engine which is one of several methods of "warming up" your catalytic converter.