Having recently replaced my radiator, thermostat, and then water pump, in that order, on my '85 300D, I can state with confidence that by far the biggest factor of the three in determining running temperature is the water pump. After replacing the first two, it was still hitting 110 C, even with a 71 degree C thermostat. After a new water pump (the old one had moderate resistance when turning the shaft by hand, with the pulley removed; the new one spun freely), I could not make it rise above 85. This was with air temperature around 65. The only difference in going to an 80 C thermostat is, with an 80 C 'stat the minimum op temp warm was 80. With the 71 C, around 78.

(I write of the car in the past tense because, on the night of September 28/29 I hit a deer in it, so, it is currently non-operational).

Tell me more about this BMW 88 C switch...