Instead of installing parts till it's fixed. Why not just have the cooling system pressure checked for leaks.
With a Stant pressure tester you will need them to have the Stant #12030 radiator adapter to hook up the pressure tester.
I know AutoZone loans out tools for free (with a refundable deposit). Not sure if they have pressure testers though.
I'm sure a shop would not charge to much to check it.
1991 525i M50 5 Sp.
N.California
America is all about speed. Hot, nasty, badass speed. -Eleanor Roosevelt