The old style will just be a NTC thermistor (temperature controlled resistor).
On many cars there is a voltage regulator on one side of the gauge, this provides a stable power supply (normally around 9-10 volts). The output of this is connected to one side of a gauge which is itself technically a resistor. This forms the top half of a potential divider.
The other side of the meter is then connected to the sensor which forms the lower half of the potential divider.
The gauge itself (unless its a newer electronic gauge) is quite often a bimetallic strip with a winding of wire round it - when current passes through the wire it heats up the strip which then moves the needle of the gauge.
When the sensor is at a lower resistance there is more current flowing through the gauge and the needle moves higher, when there is less resistance the opposite happens.
By using a mosfet or transistor in to ground the output (input) to the gauges, by applying a small voltage to the gate (or base) of the transistor/mosfet you can effectively control the gauge.
Now lets take a practial example with some easy numbers.
Assume the meter itself has a resistance of 50 ohms, the onboard regulator gives out 10v and your sender has a resistance of 50 ohms.
You then have a potential divider of 100ohms, the voltage from ground to the middle of the divider is 5 volts and you have a current of 100ma flowing through the gauge. If you can use a transitor or MOSFET with an opamp as a comparator instead of the sensor, feeding the opamp with 5v on a comparator pin will make the opamp try and keep the voltage on the other comparator pin at 5v emulating the sensor.
It all gets a bit tricky when you try and match the resistance vs temperature curve of the sensor - they are notoriously non-linear and if you plot the resistance vs temperature on a graph you'll see a nice curve.
Hence using a microcontroller to perform a lookup on a table (this might not be necessary if your curves between the two sensors match and you can just bias them correctly with resistors with a simple comparator circuit). The microcontroller will look at the input voltage from your sensor/resistor divider, work out an ouput value, convert this to a voltage with a resistor network which then feeds the comparator to drive the gauge circuit.
Sounds more complicated than it might be - from personal experience it could be an easy job to do or an absolutely nightmare job to do.
At the best you might get away with a few resistors, a regulator, a transistor and an opamp, at the worst you end up with a few days worth of messing about with programming a microcontroler, input protection circuitry and plenty of caffeine.
Where abouts are you located out of curiousity ?
Dom