OK, so I did some measurements on the tach and the thermistor.
The Tach meter movement itself is about 72 ohms (at 68 Deg F, room temp)
The thermistor itself, then when paralleled with the fixed 56 ohms is:
450 Ohm @ 40F (5C) = 50 Ohm total
210 Ohm @ 68F (20C) = 44 total
170 Ohm @ 81F (27C) = 42 total
112 Ohm @ 95F (35C) = 37 total
66 Ohm @ 113F (45C) = 30 total
Note that a moving coil meter responds constantly to a constant current, but the circuit applies a Voltage (pulsed, but a volatge pulse). In order to maintain calibration, the resistance of the coil plus series resistance added must remain constant. But the meter coil is copper which has a positive temp coefficient of 0.4% per deg C. So the neg tempco thermistor is an attempt to compensate for the Copper coil.
Over the above noted temp range, the coil resistance varies from 68 ohms (@40F) to 79 ohms (@113 F). If the series resistor were fixed at 44 Ohms (instead of the 56 Ohms plus thermistor combo) the total resistance (Series Res plus coil res) would vary from 112 to 123 ohms over those temps. Assuming the Tach was calibrated at around 68F, that would cause the meter to read about 3.5% High at 40F. And it would read about 5.7% low at 113 F.
With the compensation factor of the thermistor this reduces the variation (and in fact reverses it - a bit of "overcompensation") to a range of about 118 (@40F) and 109 (@113 F). Again assuming the tach is calibrated at 68F, this causes the tach to read about 1.7% Low at 40F and about 6.4% High at 113 F.
Soooo. It seems that the compensation from the thermistor may help in the range from 40 to 80 deg. Probably about what the English designers had in mind. But for some of us who drive in warmer climates, or those of us who only drive their Alpines on warm sunny days, and who have a hard time keeping the driver's compartment cool, this tach compensation does not seem to help much. In fact it may hurt. So I think Bernd has a valid point. You can leave it out. Maybe replace the 56 ohm resisitor with a 47 ohm. And maybe calibrate your tach at some elevated temp, close to what your behind-the-dash temp gets to when driving.
I wish I had done this earler. Next time I have my tach apart I think I will leave the thermistor in place, but I'll put a 33 ohm resistor in series with it, to reduce the compensation by about half, which should get it to just about even.
So Tracy, tell your guy to replace the 56 Ohm with a 47 ohm, and remove the thermistor. Then have him calibrate the tach at some temperature that is close to what you have inside the driver's compartment most of the time.
And Rich (Rootes), sorry but I'm still an analog guy!
Tom