I would not call a larger radiator 'band aid' either. Change the temp sensor. My road cars sit at exactly half not matter how hot outside with or without air con running. Once a sender has been cooked they are unlikely to be as accurate.

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Good - Fast - Cheap: Pick any two.
Current:
E23 735i; E30 318i; E32 735iL; E38 735iL; R50 Cooper; R55 Cooper Clubman.
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E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i