I thought I had the similar problem, but I was able to fix mines yesterday. I thought my problem was the head gasket after replacing the thermostat and waterpump
My 98 318ti overheated in the I-10, had it towed turned out the water pump bearings broke then cause the belts to snapped.
Replaced the waterpump
here the pic of the old one background car is a 325i
Bought new belts then found out the Pulley on the top left near the Alternator Pulley came off don't know why. So I have to order a new pulley
Got everything fixed up then the coolant won't circulate, since the heater was not working, thermostat was the problem. Remove everything turned out the thermostat was broken as well.
Got everything fixed and up and ready to go turned out the plastic radiator decides to break with all the heat. Decided to replace all the hoses.
Bought a radiator replacement. Fixed everything up the coolant circulate, heater works, and everything is up and running
Parts I used. total is $514 in cost, but everything in the cooling system is up and working again.
Radiator - $165
Water Pump - $70
Radiator Hoses - $60
Thermostat with housing gasket - $ 79
Coolant - $20
Engine Belts x2 - $60
Pulley - $35
Pulley Spacer - $15
Pulley Bolt and Cover - $10