I don't see how that is possible. Three, maybe, but there are an infinite number of logarithmic curves you could plot through two points.
Yes you would need three points to find an exponential function that would fit those points over a limited temperature range - you could also fit a parabolic function, polynomial function and many others. I used the NCT thermistor function which actually needs only a single parameter (B Value) to fit over the range of standard water/alcohol coolant temperatures. Since there were more than a single point and all points had some variance from a perfect NCT thermistor function curve, I used all points to find the fit with the least total squares deviation.
My point was that the two curves are different with different B values and thus requiring differnt logic circuits to produce the same voltage/temperature linear output to feed to the gauge (a linear device). The temperature sensors were not the same and should not be used interchangeably. My old Strewart-Warner experince where they used the same gauge and thermistor/module does not apply to Bosch of this period.
What I find most interesting is that Mercedes (and most manufactrurers of the period) used a linear interpolation of the thermistor gauge (wired thermistor directly to the gauge) to APPROXIMATE temperature. The approximation is further refined by placing the tick marks on the gauge at unequal intervals. The guage only indicates between 40 and 120 Celsius, so they selected a thermistor and approximated the curve with a straight line and variable tick marks over this range. Assuming they had the real temperature and indicated temperature intersect at about 120 degrees, tthen a temperature error of up to 5 degees Celsius is possible at the lower temps. The Bosch sensors had "125 degrees" imprinted on the side (maybe the B temperature?), or again assuming maybe this is where the sensors produce an accurate gauge reading?
1. The dash gauge does not produce an accurate reading with any thermistor. When guage moves off 40 - engine is heating. When gauge is in the red line - there is a problem.
2. The readings are probably most accurate on the high end of the gauge.
3. Rely on the trend instead of the numbers - increasing temperature from previous experience may indicate a problem.
4. If you want to know your coolant temperature, use an IR meter on the thermostat dome. Meter about $20 and a must for any amateur mechanic.
Unlike the old days when the temp sensor used a Bourdon tube and you could rely on the readings.