Rough Idle, but fixes with restart of engine.

[MallyE46]

Hello all, new to here and not completely sure I'm posting this right. Anyways, I have some experience working on vehicles but I'm terrible at diagnosing issues. I drive a 99 323i with 150k on the clock. I've recently replaced the expansion tank, and prior work in the past have been oil filter housing, new water pump, spark plugs, also lower and upper radiator hoses. The car drives perfectly fine but when starting up while cold, the car idles very roughly. The check engine light doesn't always come on, but when it does. It typically stabilizes and runs smooth. Car has overheated in the past but gasket has been checked and isn't blown. White smoke on start up but after car heats up, there is none. I do have a generic code reader and when ran, I get the code P0304, which is misfire in cylinder 4 I believe. Have owned the car for about 4 months now but it did sit for about half that time. Have a few guesses on what it can be, but I just want to hear some feedback from you guys, thank you to any and everyone who replies .

[nonturbodan]

I would guess a bad coil.

[MallyE46]

I would guess a bad coil.

That's what I've been thinking after doing a little research, but now I have whole completely different issue. Car is actually at the shop now

[Muzz258]

Rough idle at cold and good idle at hot usually means there is a vacuum leak between the MAF and Throttle body/Idle control valve. Check out the following

- All rubber boots and tubes for cracks or holes. The elbow tube to the ICV is a typical break point
- the hoses and tubes for the crank case ventilation system. The top tube from the valve cover and the bottom tube to the dipstick are common failure points
- The rubber blanking caps at the back of the inlet manifold, these split with age.