I had this problem. The stat opens ok but is slow to close.
Please accept my apologies for dismissing your suggestion so quickly. I'll now admit that I was prejudiced when I found that there was a BMW stat in the engine and it consists of roughly twice as much metal in the operating bits as the after market one that I had bought. Both passed the boiling water test.
HOWEVER - with SWMBO still in bed I've been playing. I've got one of her cooking pots full of water on the stove with two stats strung from the extractor fan and her jam making thermometer. What I've found is that both stats open at almost the same temperature but the old BMW one is a lot slower to close.
So whilst I'm still convinced that my fan has seen better days I will also be replacing the stat. Thank you