Have you had to add coolant recentley? If so, the overheating propblem can be caused by not bleeding the air out of the system fully.
Are all your cooling system components original? I have a 98 328i as well. I have had to replace my fan clutch, and water pump. First test your fan clutch by taking a rolled up newspaper (not a huge one) and slowly insert it into the spinning fan blade with the car running. If the newspaper stops the fan then it means the fan clutch has gone as the fan is just spinning freely. If it shreds the newspaper then its still good. The water pump impeller is made of plastic and is prone to failure over time. Sometimes it can fail without any signs, other times it can fail by imploding and causing the fan to destroy itself. not good. The Stewart water pumps are the best out their as a replacment. They pump 20% more then OEM and have a metal impeller.
Depending on your milage i would recommend doing it anyway as they are unreliable past 100,000miles. Mine lasted to almost 200,000
Give this link a read. Its not a 328i, but it shows how the pump can fail
Notes on replace water pump 1991 318i (E36) - Bimmerfest - BMW Forums
Heres a DIY on how to replace your water pump:
u n d e r s t e e r . c o m 
Linear Mode
