Is the climate control system on at this time? If on, the aux. elec. fan should come on as well to stabilize temp. You might have a weak pressure cap. Very seldom are they tested and/or replaced. Might have wrong percentage of coolant to water ratio also. Keep in mind, given what you've said it is NOT hot.

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81 300CD (sold) 1972 280 SEL 4.5 (sold) 1966 250 S 4 spd (sold) 1974 450 SL (sold) 86 BMW 325ES (sold), 1973 280C (sold) 1988 300 SE.