I think you may be able to get it to work with a transistor and a few resistors.
NPN transistor; emitter to - (0V) via a 100 ohm resistor.
Collector to gauge input, the sensor + terminal.
New sensor also connected to 0V and +12V power.
Output from the to the transistor base via a preset pot, eg. 10k, one end to 0V, other end to sensor o/p, with a 1K resistor between the pot wiper and transistor base.
Another 10K preset across 0V & 12V, wiper to the transistor base via a 10K resistor.
The first pot should adjust the "span", how much effect a temperature change has on the gauge.
The second pot adjusts the offset, eg. what the mid point temperature will be.
The two will be rather interactive and it will take several attempts to get them both in appropriate positions; you mal also need to try different values for the summing resistors to the base, if one or the other pot is at the end of its travel..
More complex solutions would be more controllable, but if it's just a one-off it should be OK once calibrated.
If it works OK but fine adjustment is difficult, you could use multiturn presets. Set them to the same position as the old post using a meter, if you do change them..
For a vehicle, it will probably need a voltage regulator to feed the offset bias pot (and possibly temperature sensor), to avoid drift as the battery voltage changes. a 78L05 should be OK for the pot supply, though that may also need a lower value resistor from the offset pot to transistor base eg. 4k7.