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.
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL (X 2 - 1 Alpine White and 1 Glacier Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i