I have just had the same problem fixed.
Ive got about the same amount of miles as you,
but have 318i on 97 plate.
I noticed a small amount of white stuff, about 6-8 inches up, from the bottom of the dipstick.
The water pump is positioned about 2cm away from the head gasket seal on my engine.
The water pump seal had broke, there fore allowing water to get to the head.
I luckily caught it in time, and i still had to have a head skim,(it was off by 4 degrees)
A new head kit, and fifteen hours of my engine slaves hard work.
Cost me nearly £650.
Apparentley my water pump has a ceramic float, which obviously if it gets to hot will crack.(not sure if yours is the same, but would guess it is)
The thermostats on E36, generally break at some point.
Causing erratic temperature readings.(they useually get stuck)
Another possibility is trapped air in the cooling system.
E36 are a little tricky to bleed.
Has to be done twice sometimes.
Therefore if it wasnt done properly previously .....
Hope i havent shit you up,
but also hope this information is useful.