1998 BMW 528 Rough start when cold only

Hi, I had the same problem with my 528i. It took me weeks to figure out what it was. What you are describing sounds very similar to my problem. Mines turned out to be a faulty Coolant Temperature Sensor. What happens is when the engine is cold the faulty temperature sensor cannot tell the engine it needs a little more fuel to start. This causes the idle to shutter and hesitate. Engines need more fuel when they are cold and a little less when they are warm/hot. This could explain why it only happens when it is cold. I am not saying this is your problem, but it could not hurt to check it out. I took mine to the mechanic and they wanted to charge me $240 to fix the problem. Luckily I figured out it was a $19 Coolant Temperature Sensor that only took about 5 min to replace. The part number I believe is 13621703993. One word of caution is when replacing the switch do not screw it in too tight. The tip is made from hallow copper and if you tighten it too much you will break it right off. Best suggestion, snug, but not too snug. Go to realoem. Com type in the part # and get a image of where the temp sensor is located. Good Luck